Copper is certainly ground. Red should be right. I think all manufacturers follow that colour code. I know sennheiser do at least, and have red as right, green as left and copper is ground.
You can trial and error, by loosely placing each of the wires in each of the 4 poles without soldering, then testing before soldering. Can be tricky to do without having excess wires touch. I've done that in the past when I haven't been sure which wire is for which channel; although that was with 3 pole jacks.