Palmprint representations using multiple filters followed by encoding, i.e. OrdiCode and SMCC, always achieve promising recognition performance. With the similar architecture but distinct idea, we propose a novel learnable palmprint coding representation, by integrating the two recent potentials, e.g. CNN and supervised Hashing, called as deep convolutional features based supervised hashing (DCFSH). DCFSH performs the CNN-F network to extract palmprint convolutional features, whose 13-layer features distilled by the PCA are used for the coding. To learn the compact binary code, the column sampling based discrete supervised hashing, which directly obtains the hashing code from semantic information, is employed. The proposed DCFSH is extensively evaluated by using various code bits and samplings on the PolyU palmprint database, and achieves the verification accuracy of EER = 0.0000% even with 128-bit code, illuminating the great potential of CNN and Hashing for palmprint recognition.