Dextromethorphan, the molecule, does plenty of stuff to your brain all by itself. It's an SNRI like a lot of anti-depressants. People who concentrate and abuse it are usually after the NMDA receptor antagonism, which is about ten times stronger with the metabolite dextrorphan.
So yes, you need a functioning CPY2D6 to convert DXM to dextrorphan. In that sense, it's a bit like codeine, which requires CYP2D6 to convert it into morphine.
Like with codeine, if you find you aren't getting "high" enough with your dextromethorphan, chances are you're also taking other drugs or foods that are interfering with this liver enzyme, maybe even on purpose because you think you have a "high drug metabolism".
Since DXM often comes with other cold medicine, I'd make sure you aren't also getting a lot of antihistamine, which could slow the conversion a bit.