SPHERE (Spectro-Polarimetric High-contrast Exoplanet Research) is a second generation VLT instrument aimed at the direct detection of exo-planets. It has received its first light in May 2014. ZIMPOL (Zurich Imaging Polarimeter) is the imaging polarimeter subsystem of the SPHERE instrument. It's capable of both high accuracy and high sensitivity polarimetry but can also be used as a classical imager. It is located behind an extreme AO system and a stellar coronagraph. ZIMPOL operates at visible wavelengths which is best suited to detect the very faint reflected and hence polarized visible light from extra solar planets. During the SPHERE fourth commissioning period (October 2014) we have made deep coronagraphic observations of the bright star alpha Gru (mR = 1.75) to assess the high contrast polarimetric performance of SPHERE-ZIMPOL. We have integrated on the target for a total time of about 45 minutes during the meridian transit in the Very Broad Band filter (600 - 900 nm) with a classical Lyot coronagraph with 3 λ/D radius focal mask. We reduce the data by a combination of Polarized Background subtraction, Polarimetric Differential Imaging (PDI) and Angular Differential Imaging (ADI). We reach contrasts of 10-6 and 10-7 at a radial distances of respectively 7 and 14 lambda/D from the PSF core. At these radial distances we are respectively a factor of 10 and 2 above the photon noise limit. We discuss our results by considering the temporal and spatial speckle behavior close to the PSF core in combination with low order polarimetric aberrations.