Pro tip: If you want to design a button matrix encoder, build one column first.
~ Design
~~~~~~~~~~~~~~~~~~~~~~~
Convert 1-of-4 to 2 bits for latch input. Separately, find pressed signal to load latch. Ignore multi-push problem; if the user wants to be silly, it's not our problem. :3
Relies on the pressed signal having a longer propagation delay. When I changed it to use one 4-input OR gate made out of diodes and a resistor, I had to add an R-C delay circuit.