  We present a new phenomenological Nucleon-Nucleon chiral potential fitted to
925 pp and 1743 np scattering data selected from the Granada-2013 NN-database
up to a laboratory energy of $125$ MeV with 20 short distance parameters and
three chiral constants $c_1$, $c_3$ and $c_4$ with $\chi^2/\nu = 1.02$. Special
attention is given to testing the normality of the residuals which allows for a
sound propagation of statistical errors from the experimental data to the
potential parameters, phase-shifts, scattering amplitudes and counter-terms.
This fit allows for a new determination of the chiral constants $c_1$, $c_3$
and $c_4$ compatible with previous determinations from NN data. This new
interactions is found to be softer than other high quality potentials by
undertaking a Weinberg eigenvalue analysis. We further explore the interplay
between the error analysis and the assumed form of the short distance
interaction. The present work shows that it is possible to fit NN scattering
with a TPE chiral potential fulfilling all necessary statistical requirements
up to 125 MeV and shows unequivocal non-vanishing D-wave short distance pieces.
