"... for Dungeons and Dragons" ah yes, I use a D16 all the time when playing D&D /s
If the d12 is for the great axe, then the d14 is for the greater axe and the d16 is for the greatest axe.
I'd be a little worried that I might be tempted to unconsciously order the values in some way which would bias the results. But you could build a box with four separate cells and a clear plexiglass top, shake them all up, and always read left-to-right or right-to-left! Sounds like a fun weekend project!