Neural network-based encoder and decoder are one of the emerging techniques for image compression. To improve the compression rate, these models use a special module called the quantizer that improves the entropy of the generated representation. Here, we propose a novel binary quantizer and an auxiliary support module known as the remapper that co-ordinate for better compression and decompression of an image. The proposed quantizer generates the compressed binary representation whereas the remapper aids in minimizing the reconstruction error during decompression. The combined optimization of the model consisting of the encoder, quantizer, remapper, and the decoder as a single entity is not feasible due to the non-differentiable nature of the quantizer. To mitigate this, we propose a step-by-step training process wherein the encoder and decoder are trained first, then keeping the encoder parameters fixed, the remapper is trained along with the decoder to obtain a fully optimized model. The training is performed with different types of images and the results are compared to understand the best training procedures. Experimental results reveal that the proposed model can compress a 256 × 256 × 3 image to a mere 256 bits, thereby achieving a compression ratio of 6144:1; with excellent perceptual reconstruction during decompression.