The electromagnetic congestion due to the continuous growth of spectral demand has been skyrocketing for the past years. Joint radar-communication systems are thus attracting attention as they can alleviate the spectrum occupancy by using the same bandwidth to perform both applications. In this context, a cooperative radar-communication system, which is a specific category that uses communication codes to both transmit information and perform radar missions, can be considered. Continuous phase modulated (CPM) codes are considered in this article in order to generate high resolution radar images from an airborne radar. Since mitigating the sidelobe level energy is essential for good image quality, we resort here to optimized mismatched filters. A fast algorithm is proposed to minimize the computational time of these filters. Simulated data are generated, as well as re-synthesized SAR images, reconstructed from real chirp-based data, using CPM codes and mismatched filters. Their performance is evaluated using different comparison tools, and shows that the use of mismatched filtering and different messages embedded in the phase of each transmitted code, provides enhanced image quality.