If it turns out that it IS the cannabis offence, then you'll probably be told that you have to ask for a character waiver.
http://www.immigration.govt.nz/opsmanual/35058.htm A5.25 b.
I think it wouldn't be a bad idea to email your CO explaining what this offence was, and the circumstances, and how long ago. It may be that that will be sufficient, but if the CO has any doubt, s/he will tell you you must apply for a character waiver. This is the same kind of letter, telling NZ that your attitude has totally changed and you regret the offences (basically, a grovel), submitted with character references from people of some standing in the community who know you now and are prepared to say that you are a law-abiding citizen. There are people on the forum who have received character waivers for much more recent and potentially serious issues. Here is a whole string of threads where people have mentioned this situation.
http://www.google.co.uk/search?hl=en...&aqi=&aql=&oq=