For many applications, path planning algorithms are expected to compute not only feasible paths, but good-quality solutions with respect to a cost function defined over the configuration space. Although several algorithms have been proposed recently for computing good-quality paths, their practical applicability is mostly limited to low-dimensional problems. This paper extends the applicability of one of such algorithms, T-RRT, to higher-dimensional problems. To this end, we propose to introduce ideas from the ML-RRT algorithm, which can efficiently solve high-dimensional path planning problems by relying on a hierarchical partitioning of the configuration space parameters. Simulation results show the good performance of the new costmap planner, MLT-RRT, for solving problems involving up to several hundreds of degrees of freedom.