Fill a pot with water, salt it, and bring to a boil. Add the wheat berries and cook, covered, about 1 hour until tender. Drain the wheat berries, rinse them unde cold water to cool, drain, and place in a bowl.
Meanwhile, bring a small pot of water to a boil, salt it, add the zucchini and cook until tender-crisp, about 1 minute. Drain the zucchini, reserving the cooking water, and rinse the squash under running cool water. Drain again an add to wheat berries.
Add the dried tomatoes to the reserved zucchini water and let stand about 10 minutes until soft. Drain and finely chop the tomatoes.
Mix them with the fresh tomatoes and add the tomato mixture to the wheat berries.
In a small bowl, whisk together the vinegar, oil, garlic, 1/4 teaspoons salt, and pepper. Pour the dressing over the wheat berry mixture and toss to coat. Cover and refrigerate for up to 3 days. Toss shredded basil in just before service.