In this paper, we present a two-dimensional dynamic metasurface aperture to perform computational polarimetric microwave imaging for the first time. First, a novel tunable dual-polarized metamaterial radiator element integrated with two PIN diodes is designed to radiate and capture cross-and co-polarized field components. The diodes placed in orthogonal positions are simultaneously switched on or off to configure the transmit and receive polarization states. In on state, the element radiated power is high whereas in off state, the element radiated power is low. By sparsely reconfiguring and random assignment of the developed metamaterial elements across the array aperture, dynamic modulation of the radiated fields is achieved. Using this principle, we synthesize polarimetric, spatio-temporally incoherent wave-chaotic modes that facilitate polarimetric computational imaging. Leveraging the novelty of the dual-polarized dynamic characteristics of the wave-chaotic radiation, polarimetric imaging is computed in the near-field region at K-band frequencies and the polarimetric responses of specific targets are retrieved. The approach is verified by electromagnetic full-wave simulations, and imaging a T-shaped object consisting of two orthogonal metal strips, it is demonstrated the target characteristics from a set of backscatter measurements compressed by the developed dynamic metasurface antenna can be retrieved both in co-and cross-polarimetric channels.