I'll try to email you a file of codes. It will include this one, which I think is your power button:

Device Code: 00.9F Function: 57
0000 006D 0022 0002 0157 00AC 0015 0016 0015 0016 0015 0016 0015 0016 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0041 0015 0041 0015 0016 0015 0016 0015 0041 0015 0041 0015 0041 0015 0041 0015 0016 0015 0041 0015 0016 0015 0041 0015 0016 0015 0016 0015 0016 0015 0016 0015 0041 0015 0016 0015 0041 0015 0016 0015 0041 0015 0689 0157 0056 0015 0E94

My interpretation of that lirc file is that it is nec1 protocol with device=0.159 and the function numbers seem to match what you posted in that picture.

The function numbers in the file I sent should correspond to the ones in the picture you posted. To convert between the numbers in that form and the numbers in the lirc file:

Look at just the last two characters on each function line of the lirc.
Translate those according to the rules
0 <--> F
1 <--> 7
2 <--> B
3 <--> 3
4 <--> D
5 <--> 5
6 <--> 9
8 <--> E
A <--> A
C <--> C
Reverse the sequence of the two.

For example, "Home" in the lirc file is 1D, which translates to 74, reverses to 47, which matches the value shown in the picture.