We outline the algorithm for computing the minimum weight of a linear code over a finite field that was invented by A. Brouwer and later extended by K.-H. Zimmermann. We show that matroid partitioning algorithms can be used to efficiently find a favourable (and sometimes best possible) sequence of information sets on which the Brouwer-Zimmermann algorithm operates. We present a new algorithm for computing the minimum weight of a linear code. We use a large set of codes to compare our new algorithm with the Brouwer-Zimmermann algorithm. We find that for about one third of codes in this sample set, our algorithm requires to generate fewer codewords than the Brouwer-Zimmermann algorithm.