Do I have any chance of going back into the Guard with an RE-3 code?

PFC (Join to see) If it was for a medical reason, you will need a novel of documentation regarding said condition and proof that it no longer is an issue. You will need:
1) a kickass recruiter who won't disappear at the first sign of difficulty w/ your packet
2) a waiver just to go to MEPS
3) MEPS to clear you
4) a Surgeon General's waiver to re-enlist

Those are the steps I had to take to get back in w/ an RE-3 Code due to a medical discharge. It took me almost 16 years to find a recruiter who wasn't scared to take on my packet.

No I passed basic was discharged in my unit

I see that you were NG. If you stay at that level, it’ll have to get cleared multiple steps before it even reaches Recruiting command. The battalion and Brigade level commander would have to sign on passing your waiver through or denying it. And then if they sign it would get forwarded to your state TAG (adjutant General) for their approval and then it would go to the recruiting command. Your chances may be slim but it’s worth a try.