VISA FORMALITIES

Are you New Zealand citizens or do you have ties with another country or in the EU?
For work as a non EU national and to live you will need both a residence and work visa and likely wont be issued one without the other. Add to that to normally get a work visa you will need an employer to prove that you can do a job that no other EU national can.
And even if you are an EU citizen finding a job will not be easy given the over 26% unemployment rate.

Either way for a definitive answer you will need to contact the Spanish embassy in Wellington as that is who will have all the exact information and will issue the visas.
Frustratingly but in an entirely normal way for all things Spanish I can't actually find a website for the Wellington embassy but they do have a contact email which is [email protected]

Still,anything is possible but the best start is at the Spanish embassy in Wellington.