The exponential increase in storage demand and low lifespan of data storage devices has resulted in long-term archival and preservation emerging as a critical bottlenecks in data storage. In order to meet this demand, researchers are now investigating novel forms of data storage media. The high density, long lifespan and low energy needs of synthetic DNA make it a promising candidate for long-term data archival. However, current DNA data storage technologies are facing challenges with respect to cost (writing data to DNA is expensive) and reliability (reading and writing data is error prone). Thus, data compression and error correction are crucial to scale DNA storage. Additionally, the DNA molecules encoding several files are very often stored in the same place, called an oligo pool. For this reason, without random access solutions, it is relatively impractical to decode a specific file from the pool, because all the oligos from all the files need to first be sequenced, which greatly deteriorates the read cost. This paper introduces PIC-DNA - a novel JPEG2000-based progressive image coder adapted to DNA data storage. This coder directly includes a random access process in its coding system, allowing for the retrieval of a specific image from a pool of oligos encoding several images. The progressive decoder can dynamically adapt the read cost according to the user's cost and quality constraints at decoding time. Both the random access and progressive decoding greatly improve on the read-cost of image coders adapted to DNA.