  We present a detailed strong lensing (SL) mass reconstruction of the core of
the galaxy cluster MACSJ 2129.4-0741 ($\rm z_{cl}=0.589$) obtained by combining
high-resolution HST photometry from the CLASH survey with new spectroscopic
observations from the CLASH-VLT survey. A background bright red passive galaxy
at $\rm z_{sp}=1.36$, sextuply lensed in the cluster core, has four radial
lensed images located over the three central cluster members. Further 19
background lensed galaxies are spectroscopically confirmed by our VLT survey,
including 3 additional multiple systems. A total of 31 multiple images are used
in the lensing analysis. This allows us to trace with high precision the total
mass profile of the cluster in its very inner region ($\rm R<100$ kpc). Our
final lensing mass model reproduces the multiple images systems identified in
the cluster core with high accuracy of $0.4"$. This translates to an high
precision mass reconstruction of MACS 2129, which is constrained at level of
2%. The cluster has Einstein parameter $\Theta_E=(29\pm4)"$, and a projected
total mass of $\rm M_{tot}(<\Theta_E)=(1.35\pm0.03)\times 10^{14}M_{\odot}$
within such radius. Together with the cluster mass profile, we provide here
also the complete spectroscopic dataset for the cluster members and lensed
images measured with VLT/VIMOS within the CLASH-VLT survey.
