Why do you need to patch the software, is it to fix problems or implement new functions?
To write patches, you must be familiar with Motorola 68xxx assembly language. Not too difficult.
However, you also need the PLEX database (including the patch data) for each MD110 release you want to write patches for but this is restricted to Aastra internal use only.
Ideally you should also have training but this too is for Aastra internal use only.
Patching MD110 is a skill which I believe is in very low demand. (Nobody has asked me to do any for a long time) so you might better spend your time learning a more useful skill like website coding or C# etc.
Bottom line is, I believe that you will find it impossible (should not really use that word I know) to gain the right tools and knowledge to patch MD110.