Genus is less specific than species, not more, so if you are allowed 9 of each genus, then it is a max of 9 chickens and junglefowl (both within the genus gallus). If the code specifically said you are allowed 9 females, that means that you are not allowed males. When code enforcement said nine of each type, she likely meant 9 of each kind of animal: chicken, turkey, goose, etc. Not 9 of each breed, which would be very unusual wording for code. About the only time code ever has anything to say about breeds, it is usually in relation to disallowing certain breeds that are considered dangerous by many.
If you provide us with the exact language of the zoning and ordinances, we can help you correctly interpret what you are allowed.