Multi pin continuity tester

What are you trying to test?
If it's only overall continuity, that can be done with a dummy plug and a dummy socket wired so that all leads are connected in series. That, however, won't identify which lead, if any, is broken.
I don't understand where your 54 pins come from. Left chanel, right chanel and ground =3
3 x 16 = 48. Where do the other 6 pins come from?