X-ray phase-contrast imaging (PCI) is sensitive to the phase shift of X-rays induced by the sample. This is advantageous for low X-ray absorption samples, such as polymers, biomaterials, tissues, and scaffolds. We show propagation-based phase-contrast X-ray computed tomography (CT) imaging [propagation-based imaging (PBI)] in a specific configuration with the wide-cone angle (>50°), polychromatic X-ray source, and a flat-panel detector. We demonstrate PBI on measurements with a polymer composite. The experiments show a tradeoff between high signal-to-noise ratio (SNR) acquisition at very large cone angles and low-SNR acquisition at large propagation distances. The degree of data quality improvement by phase retrieval increases for high propagation distances. We show the application of PBI on macroporous synthetic hydrogels, which represents an important type of material with a complex 3-D morphology in the field of polymer science. With the use of the above-described experimental configuration, it is possible to visualize the hydrogels and segment the structure of the sample in tomographic data. The segmented sample can be used for morphology characterization, such as the description of internal space or determination of specific surface area (SSA).