To clean it: Tooth brush and some aerosol spray, like BreakFree, or even simple brake cleaner. The aerosolized spray will help work under the dirt and lift it out of the crevices of the matte finish. The toothbrush will work it off the gun without letting it settle back in.
To revive a well-worn finish: Have it bead-blasted on low/moderate air pressure. Will restore the matte finish to places it has worn flat without penetrating the nickel finish.
These finishes are more fragile than blue for cosmetic concerns, but they are attractive and protective.