Weber Manuals - browse product manuals by entering a serial number or product description.
edit: wow I'm dumb, it says Silver right on the handle. So yeah, definitely a Genesis Silver. Just don't know the differences between the specific models. Something from the 90s is my best guess. The good news is you'll easily be able to find parts for it (grates, flavorizer bars, etc) and restore it into a real workhorse (or give it to a buddy who likes gas grills more than you and make them super happy.)
Except for the dirt it looks good. If the frame is solid it should clean up real nice. Check the crossbar on the left beside the grey side table to see if it is rusted through. Bruce has posted a how to video if it needs replacing. Good find and Good luck restoring it. Post lots of pictures.