Thaw the cod completely if frozen. Preheat the oven to 350°F (180°C).
Place the cod portions in a baking dish and season them with salt and dried garlic.
Chop the tomatoes into small pieces and arrange them around the cod.
Add the pitted green olives to the dish and lightly season the tomatoes with salt.
Place a small piece of butter on top of each cod portion, using about 2 tablespoons (30 g) in total.
Bake for about 30 minutes, until the cod is opaque, flakes easily with a fork, and reaches 145°F (63°C) in the thickest part.
Remove the dish from the oven and grate Parmesan over the hot fish.
Serve with the tomatoes, olives, and juices from the bottom of the dish.