BENSOLVE 1 (versions 1.0 to 1.2) was a Matlab code. The first version of BENSOLVE 2 (version 2.0.0.alpha) was published on September 3rd, 2014.
An exposition of the theory and the algorithms can be found in
Andreas Löhne and Benjamin Weißing: The vector linear program solver Bensolve -- notes on theoretical background, European Journal of Operational Research 260 No. 3 (2017), 807-813, article, arXiv preprint