Cruising some old threads and found this one. I feel compelled to reply because there is bad info it. Some of the info is 100% incorrect
9773155 is a correct engine cast code for a 1964 GTO no matter is it is tripower, 4 barrel carb, auto or man transmission.
76W A-body 64 389 348 4-speed 3x2 9773155 2 GTO
76X A-body 64 389 348 3-speed 3x2 9773155 2 GTO
77J A-body 64 389 348 Powerglide 3x2 9773155 2 GTO
78W A-body 64 389 325 4-speed 1x4 9773155 2 GTO
78X A-body 64 389 325 3-speed 1x4 9773155 2 GTO
79J A-body 64 389 325 Powerglide 1x4 9773155 2 GTO
769 A-body 64 389 348 4-speed 3x2 9773155 2 GTO
789 A-body 64 389 325 4-speed 1x4 9773155 2 GTO
The correct cast number is on that block for that car.
SR is a service replacement block. The numbers after sr are supposed to be the either the partial vin or full vin of the vehicle that were supposed to be stamped onto the block by the dealer replacing the block. But this was not always done.
084 kinda looks like a date code but I can not be certain. It might be Aug of 64. It would help to know the vin of your vehicle and the build date. If the build date is after Aug of 64 the theory is out the window. But look at the vin of your vehicle and see if it matches the numbers after the sr. But hat cast code is correct for that vehicle.