If the owner fails to comply with an order to remove or demolish a dwelling, the City may cause such dwelling to be removed or demolished. Provided that placarding of the premises as set forth in Sec. 11.6.12. shall not be exercised until the Council shall have by ordinance found the property to be unfit for human habitation and which property or properties were so found described in the ordinance. Such ordinance shall be recorded in Register of Deeds of Wake County and shall be indexed in the name of the property owner in the grantor index.