I think I'd build a standard walk in style coop, and perhaps add that to an end as a predator proof portion of the run. That way, you would have a good sized coop, a predator proof area so they could come and go in safety while you sleep in on a Saturday morning.
If you add your general location, it will help folks to give climate specific advice. That is too small to be either coop or run for 4 birds but it would be an incredible brooder!