As Dave Gittins said, what route would require the use of 330 minute ETOPS? 5 and a half hours from a landing?
AKL-EZE and maybe AKL-SCL
currently only Aerolineas Argentina (to EZE) and LAN (to SCL) are flying non-stop from AKL to South America - both use A340. Similar route is flown by Qantas (to SCL and EZE) with 747s.