The minimum recommended space required for full sized chickens is 4 square feet per chicken in the coop with a minimum of 10 square feet per chicken in the run. This assumes standard management practices as most of us on here practice them.
Your coop is 36 square feet, so that gives 6 square feet per chicken in the coop. That's great. The extra room will make it better.
If your run is 6' x 12', that gives 72 square feet or 12 square feet per chicken. That is enough. But if the run is only 4' x 4', that is only 16 square feet total or 2=2/3 square feet per chicken. Not enough, even with the extra room in the coop.
plenty big enough, not sure if your going for standards or bantams but either would do fine. And i think that what they meant by "4x4 base" was that the base is made out of 4x4's, like the wood, i think...