We present a novel method for automated diagnosis of liver lesions in multi-phase CT images. Our approach is a variant of the Bag-of-Visual-Words (BoVW) method. It improves the BoVW model by selecting the most relevant words to be used for the input representation using a mutual information based criterion. Additionally, we generate relevance maps to visualize and localize the decision of the automatic classification algorithm. We validated our algorithm on 85 multi-phase CT images of 4 categories: hemangiomas, Focal Nodular Hyper-plasia (FNH), Hepatic Cellular Carcinoma (HCC) and cholangiocarcinoma. The new algorithm suggested in this paper improves the classical BoVW method sensitivity by 7% and specificity by 3%. The shift from single-phase liver data to a multi-phase representation is shown to substantially improve classification results. Overall, the system presented reaches state-of-the-art classification results of 82.4% sensitivity and 92.7% specificity on the 4 category lesion data, a challenging clinical diagnosis task.