3769716 shows up as a '58-'62, or a '60, or a '60-'62 235 block, depending on the info source. Another person recently asked about this same casting number. His was from 1961.
The engine serial number breaks down as follows:
F=Flint engine plant
0314=assembly date=March 14
A=engine type code=235 with 3-speed manual trans. used in the passenger cars.
Unfortunately, since '57, the engine serial number does not designate an exact year, and neither does the type code, which was used for several years. To pinpoint a year, you'll have to find the casting date code on the block (probably above the starter). It'll be a letter followed by 2 or 3 numbers.
The 3836848 head was used on the circa '56 and up 235's.