So first off his is for people who want to keep their gold. I'll try to tell you how I did. I'm not sure wether this is the most effective way, but it did work for me.

When first entering the vault
1) Grab all the gold bars (36 on the table and 1 by the computer)
2) Drop the gold bars by the door
3) Go through the conversation with Elijah
4) After the conversation, grab the gold bars and go the back way to get the elevator (the doorway that Elijah doesn't go through).
*I recommend saving right here*
5) Go to the doorway (the barrier should come up), look up and drop the gold bars as close to the barrier as possible. (You might drop them off the edge, that's why you have that save)
6) Fight Elijah and run through the area as usual
7) When you get to the area where you dropped the gold bars (that's on the other side of the barrier), go into 3rd person and look along the bottom of the barrier. If you placed them close enough to the barrier, there should be an option to pick them up, though it may take a little luck to find it.
8) Walk to the elevator and if you were fast enough you will make it out alive.

Hope this helps

You've never learned to let go..

I slunk out of the Vault with the 37 gold bars and trapped Elijah inside. I've learned to let go now, though.

It's easier with C4.

I do not understand people who d this, and never will.