Quantum Negativity & 4-Partite Entanglement of GHZ State

[Jufa]

TL;DR Summary

Problem quantifying the negativity of a 4-qubit GHZ state

When I computes the negativity (with the partial transpose) of the density matrix corresponding to the GHZ I obtain zero, no matter what is the partition I choose. I've read somewhere that this is because GHZ's distillable entanglement is zero, which I don't really understand because I haven't found a definition of this sort of entanglement.
I think that the reason that all the possible negativities give zero it is because the entanglement of the GHZ is solely when one considers the whole system (full 4-partite entanglement)
My question is (also if someone could explain what the distillable entanglement is): Is there a quantity I can compute on this GHZ state (and if possible on any 4-qubit state) that measures its amount of "full 4-partite entanglement"?
Thanks in advance.

 

[Jufa]

May be it is a good idea to give a little bit of context of the problem I am facing.
In few words, I am trying to reconstruct a GHZ state of 4-qbits by means of different tomography methods and, apart from computing the fidelities of the obtained estimators, I am really interested in seeing how these methods estimate the amount of entanglement.
But in order to do so I need a measure of the entangle that does not vanish for the GHZ just as negativity does (which really shocks me, because the GHZ is maximally entangled).
That's why I am asking for both a valid entanglement measure for my case of study and (may be just for curiosity) the reason why the negativity displays this behavior on the GHZ?