Do have have any covering over the dirt? Like hay or pine shavings or anything? That is a really big space for just the coop. Congratulations! Personally, I wouldn't leave it just dirt. I would have some covering over it, at least under the roosts, that will help absorb some of the chicken waste. I use pine shavings from Tractor Supply. They cost about $5 per bag and help keep the smell down. Turn them over every few days and clean it all out a couple times a year.
If you are set on just plain dirt, you are going to have to rake it out almost daily to keep the coop from smelling bad. At least that's my opinion.