Over the past years, the ever-growing trend on data storage demand, more specifically for "cold" data (i.e. rarely accessed), has motivated research for alternative systems of data storage. Because of its biochemical characteristics, synthetic DNA molecules are considered as potential candidates for a new storage paradigm. Because of this trend, several coding solutions have been proposed over the past years for the storage of digital information into DNA. Despite being a promising solution, DNA storage faces two major obstacles: the large cost of synthesis and the noise introduced during sequencing. Additionally, this noise increases when biochemically defined coding constraints are not respected: avoiding homopolymers and patterns, as well as balancing the GC content. This paper describes a novel entropy coder which can be embedded to any block-based image-coding schema and aims to robustify the decoded results. Our proposed solution introduces variability in the generated quaternary streams, reduces the amount of homopolymers and repeated patterns to reduce the probability of errors occurring. In this paper, we integrate the proposed entropy coder into four existing JPEG-inspired DNA coders. We then evaluate the quality -- in terms of biochemical constraints -- of the encoded data for all the different methods.