Starting from a femtosecond ytterbium-doped fiber amplifier, we demonstrate the generation of near Fourier transform-limited high peak power picosecond pulses through spectral compression in a nonlinear solid-state-based multipass cell. Input 260 fs pulses negatively chirped to 2.4 ps are spectrally compressed from 6 nm down to 1.1 nm, with an output energy of 13.5 µJ and near transform-limited pulses of 2.1 ps. A pulse shaper included in the femtosecond source provides some control over the output spectral shape, in particular its symmetry. The spatial quality and spatio-spectral homogeneity are conserved in this process. These results show that the use of multipass cells allows energy scaling of spectral compression setups while maintaining the spatial properties of the laser beam.