Create/Update Global Value Set using Tooling API

As mentioned by Daniel, you can develop code to create/update GlobalValueSet.

By using tooling api, we will need to make http request to endpoint (/services/data/v41.0/tooling/sobjects/GlobalValueSet). While case of insert, no need to provide picklist value set it. But while updating that we must need to provide as below.

Insert GlobalValueset:

//you would need to update picklist values here
String fieldDef = '{"Metadata":{"customValue":[{"color":null,"default":false,"description":null,"isActive":null,"label":"Ayubb","urls":null,"valueName":"Ayub"},{"color":null,"default":false,"description":null,"isActive":null,"label":"Ansari","urls":null,"valueName":"Ansari"}],"description":null,"masterLabel":"GemsofMyLife","sorted":false,"urls":null},"FullName":"Gems_of_My_Life"}';
HttpRequest req = new HttpRequest();
req.setBody(fieldDef);
req.setHeader('Authorization', 'Bearer ' + UserInfo.getSessionID());
req.setHeader('Content-Type', 'application/json');      
req.setEndpoint(URL.getSalesforceBaseUrl().toExternalForm()+'/services/data/v41.0/tooling/sobjects/GlobalValueSet');
req.setMethod('POST');
Http httpreq = new Http();
HttpResponse res  = httpreq.send(req);
system.debug(res.getBody());

Update GlobalValueSet

String fieldDef = '{"Metadata":{"customValue":[{"color":null,"default":false,"description":null,"isActive":null,"label":"Ayubb","urls":null,"valueName":"Ayub"},{"color":null,"default":false,"description":null,"isActive":null,"label":"Ansari","urls":null,"valueName":"Ansari"}],"description":null,"masterLabel":"GemsofMyLife","sorted":false,"urls":null},"FullName":"Gems_of_My_Life"}';
HttpRequest req = new HttpRequest();
req.setBody(fieldDef);
req.setHeader('Authorization', 'Bearer ' + UserInfo.getSessionID());
req.setHeader('Content-Type', 'application/json');      
req.setEndpoint(URL.getSalesforceBaseUrl().toExternalForm()+'/services/data/v41.0/tooling/sobjects/GlobalValueSet/0Nt90000000XZHw?_HttpMethod=PATCH');**//replace id with your GlobalPicklist Id**
req.setMethod('POST');
//req.setHeader('X-HTTP-Method-Override','PATCH');
Http httpreq = new Http();
HttpResponse res  = httpreq.send(req);
system.debug(res.getBody());

With things like this the documentation is the place to start - GlobalValueSet.

We can then jump over to Workbench to try it out with the REST API:

GET /services/data/v41.0/tooling/sobjects/GlobalValueSet/0Nt7F000000cIqx

I got the GlobalValueSet ID (Keyprefix 0Nt) straight from the UI when making a test record.

The gave me the raw response:

{
  "attributes" : {
    "type" : "GlobalValueSet",
    "url" : "/services/data/v41.0/tooling/sobjects/GlobalValueSet/0Nt7F000000cIqxSAE"
  },
  "Metadata" : {
    "customValue" : [ {
      "color" : null,
      "default" : false,
      "description" : null,
      "isActive" : null,
      "label" : "First",
      "urls" : null,
      "valueName" : "First"
    }, {
      "color" : null,
      "default" : false,
      "description" : null,
      "isActive" : null,
      "label" : "Second",
      "urls" : null,
      "valueName" : "Second"
    }, {
      "color" : null,
      "default" : false,
      "description" : null,
      "isActive" : null,
      "label" : "Third",
      "urls" : null,
      "valueName" : "Third"
    } ],
    "description" : null,
    "masterLabel" : "Test",
    "sorted" : false,
    "urls" : null
  },
  "FullName" : "Test",
  "Id" : "0Nt7F000000cIqxSAE",
  "DeveloperName" : "Test",
  "MasterLabel" : "Test",
  "Description" : null,
  "NamespacePrefix" : null,
  "ManageableState" : "unmanaged",
  "CreatedDate" : "2018-05-08T10:45:35.000+0000",
  "CreatedById" : "0057F000002XauUQAS",
  "LastModifiedDate" : "2018-05-08T10:45:35.000+0000",
  "LastModifiedById" : "0057F000002XauUQAS"
}

With some slight alterations that can be replayed back to create the new record.

1. Trim out the attributes
2. Trim out any other top level fields except the Metadata and FullName
3. Modify the FullName and masterLabel
4. Modify the customValue's as required.

Use Workbench to POST to /services/data/v41.0/tooling/sobjects/GlobalValueSet.

E.g.

{
  "Metadata" : {
    "customValue" : [ {
      "color" : null,
      "default" : false,
      "description" : null,
      "isActive" : null,
      "label" : "First",
      "urls" : null,
      "valueName" : "First"
    }, {
      "color" : null,
      "default" : false,
      "description" : null,
      "isActive" : null,
      "label" : "Second",
      "urls" : null,
      "valueName" : "Second"
    }, {
      "color" : null,
      "default" : false,
      "description" : null,
      "isActive" : null,
      "label" : "Third",
      "urls" : null,
      "valueName" : "Third"
    } ],
    "description" : null,
    "masterLabel" : "Test2",
    "sorted" : false,
    "urls" : null
  },
  "FullName" : "Test2"
}

Voilà -