No, there isn't a code for each level.
My suggestion would be to use your save slots and save the game immediately after solving a difficult puzzle. That way you'll be able to skip the puzzle on the next playthrough.
Also, although it's a little bit more time-consuming, you can replace your Machinarium.sol file (which saves settings and progress) with one where the game has been saved at a later point.
Here's a link to a post that contains .sol files for most of the locations in the game:
https://forum.amanita-design.net/index.php?topic=1274.0And here are a few more that aren't in that list:
Won Five in a Row .sol FileFloating Container of Oil in Correct Position .sol FileFallen Bird .sol FileIf you're unsure where to find the .sol file on your computer, take a look at the pinned FAQs on this board:
https://forum.amanita-design.net/index.php?board=13.0Hope that helps. =o)