New visualization methods can be utilized to resolve structures at resolutions that were previously unachievable. 3D images of porous materials with high resolution have been so far obtained using transmission electron tomography or focused ion beam coupled with scanning electron microscopy. For these methods, ultra-vacuum is required, and only a small volume of the sample is visualized. Here, we demonstrate the application of ptychographic X-ray computed tomography for the visualization of soft matter with a resolution of 26 nm over large fields of view. Thanks to the high-penetration depth of the X-ray beam, we visualize the 3D complex porous structure of polyetherimide hollow fibers in a non-destructive manner and obtain quantitative information about pore size distribution and pore network interconnectivity across the whole membrane wall. The non-destructive nature of this method, coupled with its ability to image samples without requiring modification or a high vacuum environment, makes it valuable in the fields of porous- and nano-material sciences enabling imaging under different environmental conditions.