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We investigate the dynamical properties of a strongly disordered micropolar lattice made up of cubic block units. This phononic lattice model supports both transverse and rotational degrees of freedom hence its disordered variant posses an interesting problem as it can be used to model physically important systems like beam-like microstructures. Different kinds of single site excitations (momentum or displacement) on the two degrees of freedom are found to lead to different energy transport both superdiffusive and subdiffusive. We show that the energy spreading is facilitated both by the low frequency extended waves and a set of high frequency modes located at the edge of the upper branch of the periodic case for any initial condition. However, the second moment of the energy distribution strongly depends on the initial condition and it is slower than the underlying one dimensional harmonic lattice (with one degree of freedom). Finally, a limiting case of the micropolar lattice is studied where Anderson localization is found to persist and no energy spreading takes place.