The term Base64 refers to a specific MIME content transfer encoding. It is also used as a generic term for any similar encoding scheme that encodes binary data by treating it numerically and translating it into a base 64 representation. The particular choice of base is due to the history of character set encoding: one can choose a set of 64 characters that is both part of the subset common to most encodings, and also printable. This combination leaves the data unlikely to be modified in transit through systems, such as email, which were traditionally not 8-bit clean.
The string to be decoded should look simliar to this:
eval(gzinflate(base64_decode('s7EvyCjg4kpNzshXUA/JyCxWAKLEPIXUisTcgpxUhbT8IoXcSoWU1OT8lNQiheLkosyCEkV1a6gOj9ScnHyF8PyinBSQIJe9HQA=')));