Before you do that, I'd ask the question, "Are you sure you'd want back in?" Not letting you back in is kind of the point, and you need to take a long, hard look at whether the military is right for you. I sympathize with your plight, but it doesn't do anyone any good if you try to get back in just to land yourself in more trouble.
That said, a code 4 is waiverable. After a few years go by you can try to appeal, write a long and heart-wrenching letter about how you've learned your lessons, and make sure you squirt some crocodile tears. However, the Army (and the military in general) isn't exactly hurting for recruits nowadays, so I wouldn't bet on it.
