Proton computed tomography (pCT) is an imaging modality that has been in development to support targeted dose delivery in proton therapy. It aims to accurately map the distribution of relative stopping power. Because protons traverse material media in non-linear paths, pCT requires individual proton processing. Image reconstruction then becomes a time-consuming process. Clinical-use scenarios that require images from billions of protons in less than ten or fifteen minutes have motivated us to use distributed and hardware-accelerated computing methods to achieve fast image reconstruction. Combined use of MPI and GPUs demonstrates that clinically viable image reconstruction is possible. On a 60-node CPU/GPU computer cluster, we achieved efficient strong and weak scaling when reconstructing images from two billion histories in under seven minutes. This represents a significant improvement over the previous state-of-the-art in pCT, which took almost seventy minutes to reconstruct an image from 131 million histories on a single-CPU, single-GPU computer.