... unless it is a DEDICATED welder circuit !
It is dedicated for a 240 circuit. You cant put 14 wire on a 20 general 120 circuit.
There are a couple provisions for some dedicated 120v and it could apply to the welder in some case but for the crowd we are dealing with here it should be a 12/20. Some of these allowed 14 ( at 240) as ungrounded conductors and required 12 as a ground.
Most of the variations and special allowances should be taken with a bit of caution ad may work fine in a supervised world. The basic reason of the plug and cord system is it takes some of the guesswork out of it for the avg user.
You can turn a 140 machine up far enough to trip a 20 especially if one runs a larger wire in it. The move to inverters makes for more output while being less demanding on the existing wiring.
The circuit could be modified to run above 20A provided it was exclusive to that machine and not part of a general.
I am a big fan of diy wiring for one reason. 1st a simple circuit like this is as easy as it gets, most who ask and try do a good job and it takes any load off of existing which may be old etc or part of other circuits and connection and ideally places it on a circuit which goes from breaker to wire to receptacle.