Break up the cod into small flakes and season lightly with table salt if needed. Cut four 8-inch squares of plastic wrap. Lightly oil 1 sheet and lay 2 pepper halves on it, shiny side down, overlapping slightly. Shape one-fourth of the cod into a tight ball and set it in the center of the pepper. Wrap the cod in the pepper, twisting the plastic wrap around the pepper to give it a neat round shape. Transfer to a plate, twisted end down. Repeat with the remaining peppers and cod.