Do you want locking or non-locking?
For non-locking you need a 3-phase receptacle; for locking, which is probably the better choice, use a L6-60P and L6-60R.
My Code book, which is Canadian by the way, doesn't show a 60 Amp straight plug and receptacle either; probably because the 50 amp set is used for a range.
I'd go with the locking receptacle: because 60 Amps is a lot to break under load, and this can happen if the plug is accidentally removed under load. Ranges - most people turn them off before moving; 60 amp machines, such as welders, well maybe not - mistakes happen.
Hubbell makes some exotic 50, 60, and 100 Amp plugs and receptacles; because they're for special applications they're quite expensive.
And I'd be very careful about using a 3-phase plug. If somebody plugged in a 3-phase piece of equipment by mistake, and tried to energize it, you could blow the breaker and maybe even damage the equipment. 3-phase equipment just doesn't like 1-phase supplies; motors hum, whine, sniffle, and don't do anything but heat up and destroy themselves; process equipment generally tends to blow the breaker if it doesn't blow up first.
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