codie, vociferous codex hypothetical

im making a commander deck with codie, and i was wondering that with his tap ability that lets you cast a spell without paying its mana cost, also negates the cost of an overloaded spell. lets say i cast a spell, and codies ability reveals cyclonic rift. can i cast it with the overloaded cost of 6 basic and 1 blue mana for free or do i still have to pay that?