Home Postcodes by state WA 6712 Postcode 6712 6712 is the postcode for Barrow Island, WA. Localities with postcode 6712Barrow IslandWA Postcode 6712 State or territory Western Australia (WA) Localities 1 Council area Ashburton Council area based on Australian Bureau of Statistics data (ASGS Edition 3), CC BY 4.0. Postcode 6711 · Postcode 6713