We report on the first low-energy Coulomb excitation measurements with radioactive Iπ=6- beams of odd-odd nuclei Cu68,70. The beams were produced at ISOLDE, CERN and were post-accelerated by REX-ISOLDE to 2.83MeV/nucleon. γ rays were detected with the MINIBALL spectrometer. The 6- beam was used to study the multiplet of states (3-, 4-, 5-, 6-) arising from the π2p3/2ν1g9/2 configuration. The 4- state of the multiplet was populated via Coulomb excitation and the B(E2;6-→4-) value was determined in both nuclei. The results obtained illustrate the fragile stability of the Z=28 shell and N=40 subshell closures. A comparison with large-scale shell-model calculations using the Ni56 core shows the importance of the proton excitations across the Z=28 shell gap to the understanding of the nuclear structure in the neutron-rich nuclei with N ≈ 40. © 2007 The American Physical Society.