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Then it's flat out too rich. Lean the idle needle 1/4 turn and try to rev it up and clean it out. In extreme cases, you can lift the car off the ground and rev it up to clean it out. Don't rev it hard for long, just enough to burn off what's in the crankcase. If the engine still is quitting, lean the idle needle more until it will rev without quitting. Once you're there, tune the high speed needle for best performance (revving cleanly and not cutting out), and then go back to the idle needle and adjust in small increments until it will rev up to WOT cleanly. After you think you "got it" let it idle for 10-15 seconds. If it quits when you throttle it up, the idle is too rich still. If it's a little burbly and smokey at first but cleans out and revs up nice, you're pretty much where you want it to be. Ideally you want it to ever so slightly load up after a long idle (10-20 seconds). If it doesn't load up at all after 15-20 seconds, it will end up being too lean at the bottom of the tank and probably run pretty hot. Another way to tell how the engine is running (mixture-wise) is to pull the glow plug and look at the base of it. Shiny metal means rich, brown like maple syrup is perfect, and black is lean. Ideally you want it to look brown. If you have an infrared temp gun, hit the cylinder head heatsink with it to see what temp its at when it quits. If it's below 150F, it's just way too fat and needs to be leaned down.

What at fuel and glow plugs are you using?

FWIW - if the settings are too rich, it's not uncommon to have raw fuel coming out of the exhaust at idle. It's common to see the carburetor spit fuel too in overly rich conditions, but it's usually not noticed since ground based engines really shouldn't be run without an air filter for any length of time. Airplane engines will spit fuel at WOT when set to a "perfect setting" and it's visible with a good camera. It happens due to a phenomenon called fuel stand-off or carburetor stand-off.