well done, you arrived at a correct solution by a different path.
jason quoted the program 'IRTool' above, i recommend you getting your head around that program as it will help you to identify Hex codes, and is perhaps the best first step. all you need to do is download the two files and stick them in the same folder, that way when you run it the program has a 'database' from which pull the decode.
again well done.
incidentally the code you made above is:
Protocol: NEC
Device: 7.7
Function: 153