I don't know where OC is so I have no idea what your weather is like. If it is extremely cold, a coop on the ground is usually warmer. If your climate will allow it, a raised coop the size you are talking about is usually a lot easier to clean and manage. Even if you made a 4'x4' tall enough to walk in, you would not have enough room to do anything.
OEG usually do not handle confinement well so they will need more room in the run than many other breeds.
Good luck!