Prussia produced 20 mark pieces in 1888. (KM#505, KM#515 & KM#516) The coat of arms doesn't seem to match the picture however. Since the coins were gold and the pictured coin appears corroded, could it be a fake?
Yes, looks like a replica to me. 1888 is an interesting year for German Empire coins, as three emperors (and Prussian kings) appear on the pieces. Here is one (image from honscha.de) featuring Friedrich III who was king for about three months only. http://www.honscha.de/bilder/sonstige/2229g.jpg And yes, the coins are gold (Au 900) pieces, Ø 22.5 mm ... Christian