  This paper is a first report on the determination of $\Lambda_{\msbar}$ from
lattice simulations with 2+1+1 twisted-mass dynamical flavours {\it via} the
computation of the ghost-gluon coupling renormalized in the MOM Taylor scheme.
We show this approach allows a very good control of the lattice artefacts and
confirm the picture from previous works with quenched and ${\rm N}_f$=2
twisted-mass field configurations which prove the necessity to include
non-perturbative power corrections in the description of the running. We
provide with an estimate of $\Lambda_{\msbar}$ in very good agreement with
experimental results. To our knowledge it is the first calculation with a
dynamical charm quark which makes the running up to $\alpha_s(M_Z)$ much safer.
