Test beam results of a calorimetric module based on 3×3×22 cm3 PbWO4 crystals, identical to those used in the CMS ECAL Endcaps, read out by a pair of photodetectors coupled to the two opposite sides (front and rear) of each crystal are presented. Nine crystals with different level of induced absorption, from 0 to 20 m-1, have been tested using electrons in the 50-200 GeV energy range. Photomultiplier tubes have been chosen as photodetectors to allow for a precise measurement of highly damaged crystals. The information provided by this double side read-out configuration allows to correct for event-by-event fluctuations of the longitudinal development of electromagnetic showers. By strongly mitigating the effect of non-uniform light collection efficiency induced by radiation damage, the double side read-out technique significantly improves the energy resolution with respect to a single side read-out configuration. The non-linearity of the response arising in damaged crystals is also corrected by a double side read-out configuration and the response linearity of irradiated crystals is restored. In high radiation environments at future colliders, as it will be the case for detectors operating during the High Luminosity phase of the Large Hadron Collider, defects can be created inside the scintillator volume leading to a non-uniform response of the calorimetric cell. The double side read-out technique presented in this study provides a valuable way to improve the performance of calorimeters based on scintillators whose active volumes are characterized by high aspect ratio cells similar to those used in this study.