A prototype of a luminometer, designed for a future e+e- collider detector, and consisting at present of a four-plane module, was tested in the CERN PS accelerator T9 beam. The objective of this beam test was to demonstrate a multi-plane tungsten/silicon operation, to study the development of the electromagnetic shower and to compare it with MC simulations. The Moli`ere radius has been determined to be 24.0 +/- 0.6 (stat.) +/- 1.5 (syst.) mm using a parametrization of the shower shape. Very good agreement was found between data and a detailed Geant4 simulation.