Rule of thumb is 4-5 sq.feet per bird, inside the coop - excluding nest boxes and roosts. The outdoor run should provide 10 sq. feet per bird. Your dimensions are coming up short. Crowded chickens, can be very nasty chickens - resorting to bullying, feather plucking and sometimes extremes like cannibalism. Chickens will easily fly out of your run with a height of 4 ft. - unless you put a cover over it.
Your coop will also need ventilation in fact some coops in warm climates, have two wire sides and two solid, so heat doesn't build up so badly. Please visit your state thread and find out what they recommend.