A couple of my favorites-
Simple to install and pretty inexpensive ($38.59), but reasonably secure. Put it behind a door or drape, inside a closet etc if you want the shotgun out of sight.
Homak Between the Studs Long Gun Wall Safe
Costs more ($117), more difficult to install, but pretty secure and takes up no exterior room as the door fits flush with the wall. Installs between studs that are on 16" centers. Available from various sellers, this is just the first one I found online.