The 9th edition,(latest), of Flayderman's "Guide to Antique American Firearms", states:
Spencer Repeating Rifles and Carbines;Civil War model carbine, made circa 1863-1865, 52 caliber rimfire (56-56) 22" barrel with six groove rifling;sling swivel at butt. Approximately 50,000 manufactured. Serial number range 11,000 to 61,000.

Assuing steady production, yours likey was made in 1864.