Heat grill. Cut four 18x12-inch pieces of heavy-duty foil; spray with nonstick cooking spray. Place 1 cup potatoes in thin layer on each foil piece. Sprinkle both sides of each piece of cod with flour; place over potatoes. Sprinkle with salt and lemon-pepper seasoning. Dot each with butter; sprinkle with parsley. Wrap each packet securely using double-fold seals, allowing room for heat expansion.
When ready to grill, place packets, seam side up, on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 15 to 20 minutes or until fish flakes easily with fork, rearranging packets several times during cooking time.
To serve, open each packet carefully to allow steam to escape.