What is the minimum height to a crawl space, and where did you get that information?
The Code requires a minimum of 18” clear from the bottom of wood floor framing to the ground. (See ICC Figure 403.1 (3).)

I remember seeing that the bottom of beams can’t be within 12” of the ground, but I can’t find that requirement...maybe that was in an older code. 

Btw, don’t forget you need an 18”x24” crawl space access if you go through the floor and 16” x24” access if you go through the perimeter wall. (See ICC R408.3.)

Also, you need 1/150 area ventilation without a vapor barrier and 1/1500 area ventilation with a vapor barrier. (See ICC R408.1) There is an exception for eliminating crawl space vents on one side.