Thank you for trusting your question to JA today. I am a licensed attorney with over a decade of law practice and over 20 years of experience in the legal field. I’m happy to be of assistance.
Unfortunately, the fact that you turned yourself in, while a good thing, isn't really a basis for being able to rejoin. It's probably why you got a General discharge rather than an Other than Honorable.
To get back in, you have to get that RE code changed. An RE-4 is a bar to reenlistment in any branch of service. The Marines are extremely selective and disallow entry even for waiverable RE-3 codes, but with an RE-4 all branches disallow reentry.
To get your RE code changed, you have to file a DD Form 149 with the military records corrections board and that is a very difficult process. You have to prove that the RE code given was either an error or an injustice when given. Nothing about the passage of time allows for an upgraded. RE codes are intended to be permanent.
An RE-4 code is a legally appropriate code for your separation, so you can't claim error here. That leaves you only with arguing that the RE code was an injustice, based on facts that weren't considered or other potential discriminatory factors....things you haven't really gone into in your question. Regardless, this is the only means of trying to get back into the military and even if you do get the RE code changed, you won't be able to get back into the Marines. This is because, at best, ***** ***** get your RE code changed to an RE-3, which still requires a waiver and they aren't doing waivers. You'd have to try another branch of service.
If you have any further questions, please let me know. I invite follow up questions, so use REPLY for those. If you have no further questions then good luck going forward and please do not forget to rate my service with a top-three rating so that I receive credit for working with you today. Also, feel free to request me in the future, if you have questions concerning a different matter.