Raise folding is the end of the world. you cant do that with this stack size, might be able to get away with it in a sng where you can still slide into the money. but in mtt im pretty sure this would be a massive leak.
If you're entering push/fold mode with 14bbs then I think that is a massive leak and you are severely handicapping your game. There is a lot more play in a 14bb stack than that IF you are a good player. If you get flatted your hand plays very well. by push/folding at 14bbs you are taking the maximum risk to win just 2-3bbs and you are negating your positional advantage throughout the hand, and removing any ability to outplay your opponents post flop.
If you min raise in this spot you are risking 12,000 to pick up 15,000 with a very playable suited broadway hand. Seems like a no brainer to me. Also a min-raise looks stronger than a shove here, I think.
I've noticed in a lot of other hands you've posted you are making a lot of push-fold decisions with 8-12 bb stacks. The way you avoid that is by playing 15-20bb stacks more aggressively. If you raise fold here then oh well, you are at that 10-12bb stack size that REALLY IS push fold territory. Give yourself a chance to outplay your opponents before entering push/fold land.
Think about this, if you raise JTs right here and the button has QT or KT he probably has to fold. But if it folds to QTo on the button; he now has an easy open. You're seizing the fold equity before the other players can. If they have a hand, then they have a hand oh well. Get in there, mix it up take some risks and play your playable hands.