Bob, a very nice and rare gun in a 20 ga. There were only 15 made in 20 gauge. The barrels should say Nitro Steel on the bottom where they mate up to the water table. The case colors look right and so does the wood. The checkering on the for-end did cover most of it and looks right.
The Grade 4 was only made until 1912 and was discontinued. The 20 gauge guns only came with steel barrels, but not to say that they could not be ordered with Damascus.
In 1904 it was priced at $165 with ejectors, of which this one does not have. They were a $15.00 option then.
As to value, if deemed original could bring as much as $10,000 at an auction.