In a large pot, melt butter over medium-high heat. Add onion, carrot and celery and saute until softened, about 5 minutes. Add water, tomatoes, salt, basil, thyme and pepper; bring to a boil. Stir in barley, lower heat and cover. Gently simmer for 1 1/2 hours, or until barley is tender.
Stir in frozen green beans during the last 10 minutes of cooking. Remove from heat and stir in dill weed. Serve warm.