It depends on how the original ticket was booked. If it was booked by yourself on the MH website then you should be able to upgrade it online using Manage My Booking, otherwise a call to MH will get it done. If the original ticket was booked through a TA then you need to go back through that TA to upgrade it. That would mean your company's corporate TA if they booked it.
Don't assume you will be able to upgrade the ticket to a promotional Z fare. I had a case on a KUL/AKL/KUL ticket last year where I was unable to upgrade to a particularly cheap Z fare they were promoting at the time. The upgrade had to be to a D fare (which I didn't do). And as SilverChris says, a fee may apply in addition to the fare differential.