Wordpress - Redirect Restricted Page to 404

I was able to display a 404 error by using the following code in my header.

<?php
  global $wp_query;
  $wp_query->set_404();
  status_header( 404 );
  get_template_part( 404 ); exit();
?>

To break it down:
$wp_query->set_404(): tells the wp_query this is a 404, this changes the title
status_header(): sends a HTTP 404 header
get_template_part(): displays the 404 template

Why don't you create a page that show error message and then redirect user to that page? Here is a simple way to achieve that:

Open the 404.php file and add these lines to the top of it:

/**
 * Template Name: 404 Page
 */

Create a page with 404 Page template. Then redirect users:

if ( !current_user_can('administrator') ) {
    $404_page = get_permalink( $404_page_id );
    wp_redirect( $404_page );
    exit();
}

The reason you should use a page for 404 request is: in WP 404 page actually is a page that doesn't exists, WP has to search for all of its content before returning the 404 page and that work is a waste of resource. Using a pre-configured page that might help you run your blog faster.