The collision induced by the three Beryllium isotopes, 9,10,11Be, on 64Zn target were investigated at Ec.m. ≈ 1.4 the Coulomb barrier. Elastic scattering angular distributions were measured for the 9,10Be collisions whereas, in the 11Be case the quasielastic scattering angular distribution was obtained. A strong damping of the quasielastic cross-section was observed in the 11Be case, especially in the angular range around the Coulomb-nuclear interference peak. In this latter case a large total-reaction cross-section is found, more than a factor of two larger than the ones extracted in the reactions induced by the non-halo Beryllium isotopes. A large contribution to the total-reaction cross-section in the 11Be case could be attributed to transfer and/or break-up events.