The demand for data storage has grown exponentially over the past decades. Current archival solutions have significant shortcomings, such as high resource requirements and a lack of sufficient longevity. In contrast, research on DNA-based storage has been advancing notably due to its low environmental impact, larger capacity, and longer lifespan. This has led to the development of compression methods that adapted the binary representation of legacy JPEG images into a quaternary base of nucleotides while taking into account the biochemical constraints of current synthesis and sequencing mechanisms. In this work, we show that DNA can also be leveraged to efficiently store images compressed with neural networks even without a need for retraining, by combining a convolutional autoencoder with a Goldman encoder. The proposed method is compared to the state of the art, resulting in higher compression efficiency on two different datasets when evaluated by a number of objective quality metrics.