Binary is "Base 2" numbering, like normal decimal numbers are "Base 10".
(Code is really a stray word, just as many people associate binary with computers or "computer code"...)
As each binary digit [or bit, for short] has only two values, 0 or 1, it's convenient for use in electronic switching or logic circuits that also have two states, on & off or true/false etc.
"Base 16" - hexadecimal - is also commonly used in electronic and computers, as each hex digit translates directly either way to a group of four binary digits & it's a lot more convenient that long strings of 0s and 1s..
Any number can be represented in any base. Most scientific calculators can convert between bases or at least common ones like binary, decimal, octal, hexadecimal etc.
Mostly, binary is just numbers.
"Code" can again use any number base and may relate to lookup tables where specific numbers have different meanings or work like indexes into a list, but that is not specific to binary, just numbers in general.