For $400, you'd have to go the super budget route. Honestly, I can't think of any LED grow lights with a flowering coverage area of 4x4 for that low of a price. For $450 you can get the TS3000 by Mars Hydro - that will cover a 4x4. Also, discount code MRGROWIT will give you a small percentage off
But yeah that's a tough one. I'd love to hear if anyone else has suggestions.
My list of the best LED grow lights for a 4x4 flowering coverage area: