Home Postcodes by state SA 5068 Postcode 5068 5068 is the postcode for 8 localities in SA: Heathpool, Kensington, Kensington Gardens, Kensington Park, Leabrook, Marryatville and 2 more. Localities with postcode 5068HeathpoolSAKensingtonSAKensington GardensSAKensington ParkSALeabrookSAMarryatvilleSASt MorrisSATrinity GardensSA Postcode 5068 State or territory South Australia (SA) Localities 8 Council area Norwood Payneham and St Peters; Burnside Council area based on Australian Bureau of Statistics data (ASGS Edition 3), CC BY 4.0. Postcode 5067 · Postcode 5069