Could you make penicillin?

Ok, hypothetical: you're in a post Apocalyptic world (2026) and your road warrior companion is infected with something. Could you produce penicillin all on your own?

How about if you got accidentally transported to 1348 Europe and the black death is dropping people? Could you produce it there, given access to any period-appropriate items you wanted?

How would you do it?

I know you've thought about it. All labrats think about this. It's like guys thinking about Ancient Rome or dying in battle.