I don't have the experience that Bill and Dean have however from what I have seen in the Parker Story, the engraving on the breech balls and hammers suggest a Grade 2. A clear close up of the sidelocks, underside of the receiver, and the checkering pattern of the forend would shed some additional information on this gun. There are surviving factory records so a letter may help.
On the picture of the receiver, looks like some pitting around the left firing pin hole. What is the condition of the barrels both inside and outside? Clean the inside of the barrels with some bore cleaner and a good stiff bronze brush to get a good idea of the pitting. With an unstruck barrel weight of 5lb, those barrels should have plenty of thickness.
Where are you located? I would find a local gunsmith who is familiar with vintage side by sides and get his opinion. It may be a good canidate for a restoration or you could shoot it as it is
