We introduce a natively distributed mini-application benchmark representative of plastic spiking neural network simulators. It can be used to measure performances of existing computing platforms and to drive the development of future parallel/distributed computing systems dedicated to the simulation of plastic spiking networks. The mini-application is designed to generate spiking behaviors and synaptic connectivity that do not change when the number of hardware processing nodes is varied, simplifying the quantitative study of scalability on commodity and custom architectures. Here, we present the strong and weak scaling and the profiling of the computational/communication components of the DPSNN-STDP benchmark (Distributed Simulation of Polychronous Spiking Neural Network with synaptic Spike-Timing Dependent Plasticity). In this first test, we used the benchmark to exercise a small-scale cluster of commodity processors (varying the number of used physical cores from 1 to 128). The cluster was interconnected through a commodity network. Bidimensional grids of columns composed of Izhikevich neurons projected synapses locally and toward first, second and third neighboring columns. The size of the simulated network varied from 6.6 Giga synapses down to 200 K synapses. The code demonstrated to be fast and scalable: 10 wall clock seconds were required to simulate one second of activity and plasticity (per Hertz of average firing rate) of a network composed by 3.2 G synapses running on 128 hardware cores clocked @ 2.4 GHz. The mini-application has been designed to be easily interfaced with standard and custom software and hardware communication interfaces. It has been designed from its foundation to be natively distributed and parallel, and should not pose major obstacles against distribution and parallelization on several platforms.