I would not go with a coop that small unless you lived somewhere really warm or you were sure they would never have to be in there for more than sleeping. Never. I would personally would not do it.
You don't need large coop for your 15 chickens. The 4' x 7' coop with 4-6 nest boxes will do. However, you do need a large run. Keep in mind... the predators are your chicken #1 enemy so focus more on the run to keep them safe. I wish that I have 3 acres of land and the coop will be in the center that allow me to rotate to new run as see fit. Of course, the unused run will be growth vegetable or poultry feed to cut down the cost.