I'll post photos of an 1862 dated and a 1863 dated barrel. You can see the top of that last numeral is rounded like a 2 or a 3. You'll have to judge whether the lower left side of the numeral on your gun is rounded like the "3" or has a sharp point like the "2"
The lockplate date of 1864 does not match the barrel / barrel band style - notice the early M1861 bolster on the barrel, but the M1863 type rounded barrel bands.
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View attachment 445271