The freedom of design of coded masks used by mask-based lensless cameras is an advantage these systems have when compared to lens-based ones. We leverage this freedom of design to propose a shape-preserving optimization scheme for a radial-type amplitude coded mask, used for extending the depth of field (DOF) of a lensless camera. Our goal is to identify the best parameters for the coded mask, while retaining its radial characteristics and therefore extended-DOF capabilities. We show that our optimized radial mask achieved better overall frequency response when compared to a naive implementation of a radial mask. We also quantitatively and qualitatively demonstrated the extended DOF imaging achieved by our optimized radial mask in simulations by comparing it to different non-radial coded masks. Finally, we built a prototype camera to validate the extended DOF capabilities of our coded mask in real scenarios.