The number gazillion does not refer to nor contain a specific number of zeros because it is not an actual number. Gazillion is a descriptive word, not a unit of measurement, and is used to refer to an excessively large quantity.
There are several other fictitious numbers commonly use to express large quantities, including bazillion, gajillion and katrillion. These made-up numbers sound similar to real numbers, like million and billion, because they all end in "-illion". Though gazillion is not an actual numerical term, it is an actual word in the English language and can be found in the dictionary as an adjective.