The discovery of informative itemsets is a fundamental building block in data analytics and information retrieval. While the problem has been widely studied, only few solutions scale. This is particularly the case when i) the data set is massive, calling for large-scale distribution, and/or ii) the length k of the informative itemset to be discovered is high. In this paper, we address the problem of parallel mining of maximally informative k-itemsets (miki) based on joint entropy. We propose PHIKS (Parallel Highly Informative K-ItemSet) a highly scalable, parallel miki mining algorithm. PHIKS renders the mining process of large scale databases (up to terabytes of data) succinct and effective. Its mining process is made up of only two efficient parallel jobs. With PHIKS, we provide a set of significant optimizations for calculating the joint entropies of miki having different sizes, which drastically reduces the execution time, the communication cost and the energy consumption, in a distributed computational platform. PHIKS has been extensively evaluated using massive real-world data sets. Our experimental results confirm the effectiveness of our proposal by the significant scale-up obtained with high itemsets length and over very large databases.