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With frugality spirit, I sent it via first-class-mail. It was returned because it didn't have enough stamps. I resent it 3 days late (april 18th 2018, for tax returns of 2014). Federal was not accepted, state was.

Anything that can be done? It seems I'm out of luck

Yes, you are out of luck.

If you had filed for an extension in 2015, then you would have had until Oct 2018. But that has also passed.