This article introduces a new systolic algorithm for QR factorization, and its implementation on a supercomputing cluster of multicore nodes. The algorithm targets a virtual 3D-array and requires only local communications. The implementation of the algorithm uses threads at the node level, and MPI for inter-node communications. The complexity of the implementation is addressed with the PaRSEC software, which takes as input a parametrized dependence graph, which is derived from the algorithm, and only requires the user to decide, at the high-level, the allocation of tasks to nodes. We show that the new algorithm exhibits competitive performance with state-of-the-art QR routines on a supercomputer called Kraken, which shows that high-level programming environments, such as PaRSEC, provide a viable alternative to enhance the production of quality software on complex and hierarchical architectures.