I believe it to be not only our right, but also our duty as humans to do the best we can to contribute to the advancement and flourishing of our species. What better way to survive death than by leaving a mark in the memories of our fellow human beings. Is Mark Twain dead? Einstein? Aristotle? Shakespeare?
This is the only life we've got, so we ought to live it to its fullest and make the best of it.
Not sure what makes you draw such a conclusion, it looks pretty much out of place. Since there's no deity or "higher plan" or any of that as you say, then we can't really have any duty, same as a cockroach has no duty when it runs around the kitchen. There's no reason to think our running around should be any better than a cockroach's.
Moreover, there's no surviving death either: what does it matter to Mozart that he's one of the greatest living composers now, when he died before he turned 36, suffering in pain and spending most of his life in poverty; buried in a common grave with almost no one attending the funeral. He's dead, so he can't really know anything that happened later on, can he?