If you look down at the action from the top, you'll notice that dampers do not go all the way to the last string. Usually only the first 70 or so notes have dampers. The noise you are hearing is probably the sympathetic vibration of the undamped strings. This is normal for any piano.
I be willing to bet that the room in which you keep your Schimmel is very "live" accoustically. Hard floor surfaces, few pieces of upholstered furniture, light drapes if any at all. If the ringing bothers you, I'd start adding sound absorbent materials to the room. A thick area rug or carpet, upholstered chairs or sofa, heavier drapes. If that doesn't do it, then consider hanging a quilt on the wall behind the piano.