Asparagus will tolerate a salty soil, a very unusual trait. If asparagus is the only planting in the raised bed that could work well for you. Consider Rodale's Organic Encyclopedia recommendations which talk of using salt, not for weed control, but for the health of the plant:
"For healthy asparagus, add sodium chloride rock salt (NaCl) to beds more than one year old. Apply 2.5 lb. per per 100' row either before spears appear or around July 4. Research shows this treatment helps asparagus resist crown and root rot diseases caused by Fusarium fungi and also improves overall growth. Don't use iodized table salt or rock salt made of calcium chloride (CaCl). Pickling salt, however, is fine for the job."