Age prediction from medical images or other health-related non-imaging data is an important approach to data-driven aging research, providing knowledge of how much information a specific tissue or organ carries about the chronological age of the individual. In this work, we studied the prediction of age from computed tomography angiography (CTA) images, which provide detailed representations of the heart morphology, with the goals of (i) studying the relationship between morphology and aging, and (ii) developing a novel \emph{morphological heart age} biomarker. We applied an image registration-based method that standardizes the images from the whole cohort into a single space. We then extracted supervoxels (using unsupervised segmentation), and corresponding robust features of density and local volume, which provide a detailed representation of the heart morphology while being robust to registration errors. Machine learning models are then trained to fit regression models from these features to the chronological age. We applied the method to a subset of the images from the Swedish CArdioPulomonary bioImage Study (SCAPIS) dataset, consisting of 721 females and 666 males. We observe a mean absolute error of $2.74$ years for females and $2.77$ years for males. The predictions from different sub-regions of interest were observed to be more highly correlated with the predictions from the whole heart, compared to the chronological age, revealing a high consistency in the predictions from morphology. Saliency analysis was also performed on the prediction models to study what regions are associated positively and negatively with the predicted age. This resulted in detailed association maps where the density and volume of known, as well as some novel sub-regions of interest, are determined to be important. The saliency analysis aids in the interpretability of the models and their predictions.