Abstract: Background: Neutron-rich nuclei with protons in the fp shell show an onset of collectivity around N=40. Spectroscopic information is required to understand the underlying mechanism and to determine the relevant terms of the nucleon-nucleon interaction that are responsible for the evolution of the shell structure in this mass region. Methods: We report on the lifetime measurement of the first 2+ and 4+ states in 70,72,74Zn and the first 6+ state in 72Zn using the recoil distance Doppler shift method. The experiment was carried out at the INFN Laboratory of Legnaro with the AGATA demonstrator, first phase of the Advanced Gamma Tracking Array of highly segmented, high-purity germanium detectors coupled to the PRISMA magnetic spectrometer. The excited states of the nuclei of interest were populated in the deep inelastic scattering of a 76Ge beam impinging on a 238U target. Results: The maximum of collectivity along the chain of Zn isotopes is observed for 72Zn at N=42. An unexpectedly long lifetime of 20−5.2+1.8 ps was measured for the 4+ state in 74Zn. Conclusions: Our results lead to small values of the B(E2;41+→21+)/B(E2;21+→01+) ratio for 72,74Zn, suggesting a significant noncollective contribution to these excitations. These experimental results are not reproduced by state-of-the-art microscopic models and call for lifetime measurements beyond the first 2+ state in heavy zinc and nickel isotopes.