If the date coding is the same as the later '68 - '70 carbs that I am more familiar with, 303 should be 1963, 10th month (October), 3rd week. 623 would be 1966, 2nd month (February), 3rd week.
Numerals were used for the month, so 1 is January, 0 is the 10th month or October, then A is November and B is December. Almost as if someone didn't realize they would run out of digits before they ran out of months.