Budweiser's already beer, probably won't ferment the way you expect. Basil would need a pretty high amount of alcohol in solution to extract the essence you were going for.
I have heard you can dry hop with bud to decent effect. THC is alcohol soluble as you know. So I would make up a nice barleywine maybe even an american style with lots of dry hopping. Throw in an oz. of premium bud in secondary for a week or two then package as normal. I would just make the beer at least 10 percent to better extract the "goodies" from the plant material. Also I would make it a 3 gallon batch so that a single 22 oz bottle would have a profound effect. Don't accidentally serve that one to your in-laws!