Wash cod under cold running water. Soak cod in cold water, refrigerated, overnight, changing the water 4 times. Drain and dry the cod. The fish may be cut into large bite-size chunks.
In a large pot, heat the oil. Add the fish to the hot oil and crush the fiber of the fish with the back of a wooden spoon. Add the garlic, bay leaves and olives. Saute the mixture. Add the tomato paste and stir. Add the water and bring to the boil. Skim the surface of white floating particles. Add the plum tomatoes and again bring to the boil. Simmer for 2 hours. Add the potatoes and cook for 1 additional hour. Serve the stew in bowls with crusty bread.