How do I get out of here myself?

Hint 1 of 4:

Crawling up would be a little hard.

Hint 2 of 4:

But you could probably manage to transport up.

Hint 3 of 4:

Try calling the Eureka with your communicator.

Hint 4 of 4:

Well, that didn't work, but Beatrice has given you something.