I consider that to be too small for that many chickens, I would increase the space to about 3 times as much.
Chickens can 'fit' but that won't account for stress and health at all. You'll do better if the entire flock is raised together from eggs. Siblings don't fight to work out the pecking order as much as adults put do. You won't be able to add to the flock easily at all. Any newcomer would be 3/4 killed by the stress.
Chickens need enough space to give bullies a wide berth. literally. 15 is far far too many for 4 x 8 x 7.
Adding to that coop with your skills is rather easy though.