Both of us had flown and do fly in a multi crew invironment. After the event we discussed it. My co-pilot said he was sure I said going around gear up but I am equally sure I just said going around.
I've never seen a crew environment situation in which the gear would be raised without first a statement from the PNF regarding either "Positive Climb," or "Positive Rate."
If you said "Go Around Gear UP," then the gear still shouldn't be raised until a positive climb has been achieved, you've been advised by the PNF that he has a positive indication of a climb, and that following this clarification you again state "Gear Up." Gear should never be commanded up until confirmation by the PNF has been verbally announced regarding the positive rate, and the PNF should never attempt to raise the gear until he's advised regarding the positive climb and
then received the order to raise the gear.
No matter what the pilot in the other seat thought he heard, if he didn't advise you that he had a positive climb, then receive a command to raise the gear, he had no business touching the gear handle. Assumption is the mother of screw-ups, and he very nearly gave birth to a mishap by embracing mum.
The other danger to adding to the creation of a situation like that is distraction. In this case the very poor vis and low cloud meaning that your eyes are firmly fixed out of the aircraft.
As PNF, his eyes should have been half-in, half-out, and unless you were in the process of landing, you as PF should be eyes-in. When beginning the missed approach or go-around/balked landing, the immediate transition, especially in low visibility, should be immediately back to instruments...eyes shouldn't be firmly fixed outside the aircraft. I find that the lower the visibility, the more attention I pay inside the aircraft when landing.