To help radiologists examine the growing number of computed tomography (CT) scans, automatic anomaly detection is an ongoing focus of medical imaging research. Radiologists must analyze a CT scan by searching for any deviation from normal healthy anatomy. We propose an approach to detecting abnormalities in axial 2D CT slice images of the brain. Although much research has been done on detecting abnormalities in magnetic resonance images of the brain, there is little work on CT scans, where abnormalities are more difficult to detect due to the low image contrast that must be represented by the model used. We use a generative adversarial network (GAN) to learn normal brain anatomy in the first step and compare two approaches to image reconstruction: training an encoder in the second step and using iterative optimization during inference. Then, we analyze the differences from the original scan to detect and localize anomalies in the brain. Our approach can reconstruct healthy anatomy with good image contrast for brain CT scans. We obtain median Dice scores of 0.71 on our hemorrhage test data and 0.43 on our test set with additional tumor images from publicly available data sources. We also compare our models to a state-of-the-art autoencoder and a diffusion model and obtain qualitatively more accurate reconstructions. Without defining anomalies during training, a GAN-based network was used to learn healthy anatomy for brain CT scans. Notably, our approach is not limited to the localization of hemorrhages and tumors and could thus be used to detect structural anatomical changes and other lesions.