Preheat a grill for cooking over medium heat (350 to 400 degrees F). Tear off four 15-by-12-inch sheets of aluminum foil. Arrange the sheets vertically and place a piece of halibut just below the center of each. Rub with the garlic and sprinkle with 1/4 teaspoon salt.
Sprinkle the tomatoes and corn around the halibut, distributing equally among the 4 pieces. Sprinkle the halibut and the vegetables with freshly ground black pepper.
Fold the foil over and seal upward on all sides to keep the juices in, leaving a small vent for steam to escape. Place the pouches on the grill, cover and cook until you hear sizzling, about 10 minutes. Remove 1 pouch and carefully open (the steam will be hot!) to check that the halibut is cooked through. It should be somewhat firm in the middle, and the color should be creamy opaque white. Allow the fish to rest for a couple of minutes before cutting into it.
Sprinkle with the basil and drizzle with 2 teaspoons olive oil for added richness if desired. Serve.
If the halibut skin is still intact, leave it on during cooking. The skin's good fats lend richness to the dish. After cutting the kernels off the cob, use a spoon to scrape out the "milk," for added flavor in the pouches.