ummm at first i thought you meant maybe 3s-gte or 3t-gte, in which case there is tons of info on these
but i googled "3g-gte" and stuff did come up.
assuming they weren't typo's it looks like they came in st165's around late 1987.
i wonder if it is a typo or the engine actually existed.
that's the best i could do. sorry