The whole idea of median-joining networks (when applied to evolutionary history) should be reconsidered. Are you sure it fits your expectations? For further reading see [1] http://onlinelibrary.wiley.com/doi/10.1111/cla.12147/full .
[1] Kong, S., Sánchez-Pacheco, S. J. and Murphy, R. W. (2015), On the use of median-joining networks in evolutionary biology.