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The detection and measurement of gamma-ray lines from the decay chain of⁵⁶Ni provides unique information about the explosion in supernovae. SN2014J at 3.3Mpc is a sufficiently-nearby supernova of type Ia so that such measurements have been feasible with the gamma-ray spectrometer SPI on ESA's INTEGRAL gamma-ray observatory. The⁵⁶Ni freshly produced in the supernova is understood to power the optical light curve, because it emits gamma rays upon its radioactive decay first to⁵⁶Co and then to⁵⁶Fe. Gamma-ray lines from⁵⁶Co decay are expected to become directly visible through the white dwarf material several weeks after the explosion, as they progressively penetrate the overlying material of the supernova envelope, which is diluted as it expands. The lines are expected to be Doppler-shifted or broadened from the kinematics of the⁵⁶Ni ejecta. We aim to exploit high-resolution gamma-ray spectroscopy with the SPI spectrometer on INTEGRAL toward constraining the⁵⁶Ni distribution and kinematics in this supernova. We use the observations with the SPI spectrometer on INTEGRAL, together with an improved instrumental background method. We detect the two main lines from⁵⁶Co decay at 847 and 1238 keV, which are significantly Doppler-broadened, and at intensities (3.65±1.21)x10^–4 and (2.27±0.69)x10^–4ph/cm²/s, respectively, at their brightness maximum. We measure their rise toward a maximum after about 60-100 days and a decline thereafter. The intensity ratio of the two lines is found to be consistent with expectations from ⁵⁶Co decay (0.62±0.28 at brightness maximum, the expected ratio is 0.68). We find that the broad lines seen in the late, gamma-ray transparent phase are not representative of the early gamma-ray emission, and notice instead that the emission spectrum is complex and irregular until the supernova is fully transparent to gamma rays, with progressive uncovering of the bulk of ⁵⁶Ni. We infer that the explosion morphology is not spherically symmetric, both in the distribution of ⁵⁶Ni and in the unburnt material which occults the ⁵⁶Co emission. After we compare light curves from different plausible models, the resulting⁵⁶Ni mass is determined to be 0.49±0.09M_☉.