To me this says flights with NZ code, operated by another carrier are generally ineligible for earning Velocity points. The exceptions are codeshare flights operated by Air Nelson, Eagle Airways and Mount Cook Airlines, and VA, so regional flights are OK. But not SQ operated flights :-( Which is a shame, as usually on star alliance (which VA isn't, but the SQ and NZ obviously are) it is the operating carrier that determines earn or not.

That downer aside, the easiest way to get four sectors on VA is to book four sector return flight to Australia using VA code (on either VA metal or NZ metal), such as AKL-WLG-SYD, AKL-SYD-CBR etc return).