4x4 matrix keypad - Multiple inputs cause extra readings
I have a post about keypad matrices which discusses this issue. The issue with keypads is, that if you don't install diodes, if three keys are pressed the current finds its way around those three keys and it looks like a fourth is pressed.



If you install diodes, like this, the issue goes away:



It can be a little tedious to do, but I managed it the other day with surface mounted diodes.



The above board is different from yours, mine is one with soft switches which I could lift off to get at the board.

Yours looks like it might be almost impossible to cut the tracks and install the diodes. Without them you can press two keys at once without issues. Perhaps that is enough. :)