I agree with Tom/Barb on the angle of entrance. If your builder is going by the HOA'S specs I would approach the association to see if they would let you go 16' high on the garage. Your best case is a 16 X 40 at not that much more cost. With the 12' door the contractor is going to take up 2 feet of that with door hardware. even if you use a low clearance kit on the door hardware it still wouldn't be enough for me. Being a contractor I have seen similar, that the homeowners have gone to the HOA and explained his issues and not once was turned down. I'd try for the 16 X 40. Good Luck