DNA exhibits remarkable potential as a data storage solution due to its impressive storage density and long-term stability, stemming from its inherent biomolecular structure. However, developing this novel medium comes with its own set of challenges, particularly in addressing errors arising from storage and biological manipulations. These challenges are further conditioned by the structural constraints of DNA sequences and cost considerations. In response to these limitations, we have pioneered a novel compression scheme and a cutting-edge Multiple Description Coding (MDC) technique utilizing neural networks for DNA data storage. Our MDC method introduces an innovative approach to encoding data into DNA, specifically designed to withstand errors effectively. Notably, our new compression scheme overperforms classic image compression methods for DNA-data storage. Furthermore, our approach exhibits superiority over conventional MDC methods reliant on auto-encoders. Its distinctive strengths lie in its ability to bypass the need for extensive model training and its enhanced adaptability for fine-tuning redundancy levels. Experimental results demonstrate that our solution competes favorably with the latest DNA data storage methods in the field, offering superior compression rates and robust noise resilience.