Cannot complete "Remove the Heart" Quest

OK, I found also another way that is similar to what @Marionettechaos said. What is different is that you don't need to do climbing.

After you destroyed the turret you need to follow the way to the entrance. Not the one in the cave on the right but the one on the left after the structure with the destroyed consoles.

Just before the door you can jump on the rocks and go on the top of the building where the elevator is. You can look down and see the three platforms outside the elevator room. 

Slowly you need to go down the cliff and jump to one of the platforms. This time the enemies wont be there to bother you and you can fast travel at any time. Just go and open the elevator door with the red console.

Than go back and fast travel to your ship. The rest is the same as his comment. Go out of the planet and immediately return back.

Teleport to the enemy base, destroy the turret and and use the normal way to the elevator. It should be green.

I hope that this will work for someone.

Have a nice play all.