Character ref or just more info?

Hi, 12 years ago I received a Reprimand for shoplifting (I was 16). I had to declare this on my visa application and now INZ have concerns about my character (being dishonest) and they've invite me to add more information.

Has anyone had anything similar?

I'm unsure if I need a character reference, if I do, can it be family? At short notice I don't think I can ask my recent employer.

Or is a simple, grovelling letter saying how I regret my actions, never do it again, give examples of my work in the community etc, enough?

Many thanks!

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