While the Konami Code (Up Up Down Down Left Right Left Right B A) was made popular by Contra, it made its first appearance in the 1986 NES game Gradius.
I'm pretty sure the code got popular through Gradius, to be honest. When the game was released it was mentioned pretty much everywhere, then it became a thing to try it in every Konami game.
That may be true, but I'm under the impression more people know it from Contra as opposed to Gradius - the majority of people I've known over the years always refer to the "Contra Code" or associate the code to Contra and not Gradius.