  We present a precise non-perturbative determination of the renormalization
constants in the mass independent RI'-MOM scheme. The lattice implementation
uses the Iwasaki gauge action and four degenerate dynamical twisted mass
fermions. The gauge configurations are provided by the ETM Collaboration.
Renormalization constants for scalar, pseudo-scalar, vector and axial
operators, as well as the quark propagator renormalization, are computed at
three different values of the lattice spacing, two volumes and several twisted
mass parameters. The method we developed allows for a precise cross-check of
the running, thanks to the particular proper treatment of hypercubic artifacts.
Results for the twist-2 operator $O_{44}$ are also presented.
