3-phase power to NEMA L14-20 receptacle
NEMA 14-20 are intended for two phase power.  Of the four conductors, two are energized, one is neutral, and one is ground.

  (NEMA 14-20 diagram)

A NEMA L15 is specifically intended for 3 phase power including a ground (but no neutral).  The number after the hyphen is the current rating.  That is, NEMA L15-60 is for 60 ampere conductors.

  (NEMA L15-20 diagram)

As you can see, they look vitually identical.  See the full chart here.

I can see why one would make the substitution.  The NEMA 14 is like a $25 connector.  The L15-20 is closer to $60, each side.  They both accommodate four wires.  I am sure it would not pass muster to substitute one for the other, but in a private, non-commercial, non-permanent installation where there is no possibility of intermixing the connectors with other devices and outlets, it might be okay safety-wise with durable signage present.