OP here, thanks all for your observations and information. Armed with this knowledge I asked and found out that this was actually set up for me in a hurry by someone who has since left the company, after first seeing my Model S a year ago. An unfinished and mis-done project for sure. I'm not sure it's live but will ask them to shut off the breaker if it is.
I will take your advice and get the maintenance guy to have a proper electrician check the wire gauge, put it in conduit, and replace that cobbled together box with a 14-50 box with cover. Is a 60A breaker ok or does it need to be replaced with a 50A one? (I expect the answer will be the Tesla can handle it but someone else might get an unpleasant surprise). Thanks all.