The simulation of the behavior of the human brain is one of the most ambitious challenges today with a non-end of important applications. We can find many different initiatives in the USA, Europe and Japan which attempt to achieve such a challenging target. In this work, we focus on the most important European initiative (the Human Brain Project) and on one of the models developed in this project. This tool simulates the spikes triggered in a neural network by computing the voltage capacitance on the neurons' morphology, being one of the most precise simulators today. In the present work, we have evaluated the use of MPI+OpenMP tasking on top of this framework. We prove that this approach is able to achieve a good scaling even when computing a relatively low workload (number of neurons) per node. One of our targets consists of achieving not only a highly scalable implementation, but also to develop a tool with a high degree of abstraction without losing control and performance by using \emph{MPI+OpenMP} tasking. The main motivation of this work is the evaluation of this cutting-edge simulation on multi-morphology neural networks. The simulation of a high number of neurons, which are completely different among them, is an important challenge. In fact, in the multi-morphology simulations, we find an important unbalancing between the nodes, mainly due to the differences in the neurons, which causes an important under-utilization of the available resources. In this work, the authors present and evaluate mechanisms to deal with this and reduce the time of this kind of simulations considerably.