How to set +60Hz refresh rate with an Intel CPU?

The Intel i7-4770k only supports up to 60Hz refresh rate since the onboard graphics (Intel HD 4600) only supports that. This is shown in the product specification in the screenshot below:

enter image description here

The product page is here:

So unfortunately, you're stuck at a maximum of 60Hz using the onboard graphics.

That's all it can do, 60Hz is the maximum refresh rate the on-chip GPU can achieve.

Ref: Intel Ark - Intel® Core™ i7-4770K Processor