Interesting hand, but of anything in the hand, I think 1h is the least no brainer part here, I'd go for a pass or a 2h bid, but wouldn't consider it for 1h. Needs at least another jack, but likely that's not even enough.
p- 1d - p - 2c - (2h) - p - p - 3c - 3n seems the most likely, or maybe (2h) - p - p - 3c - p - 3d - p - 3s - p - 3n?