Being of interest in the framework of the classification of discrete structures, the author applies combinatorial and algebraic methods for generating \((n,k)\) linear codes distributed uniformly at random over all isometry classes of linear codes. The main theoretical tools are the \textit{Dixon-Wilf-algorithm} (originally developed for the random generation of unlabelled graphs [\textit{J. D. Dixon} and \textit{H. S. Wilf}, J. Algorithms 4, 205--213 (1983; Zbl 0532.68064)], and the fact that isometry classes of linear codes can be represented as orbits under the group action of a wreath product. The author has implemented his algorithm in the computer algebra system \texttt{SYMMETRICA} (Uni-Bayreuth) for the generation of linear codes over prime fields. He presents some computational results on binary codes: for each pair \((n,k))\) where \(n \in \{15,16,17,18,19,20\}\) and \(k \in \{ 5,6,7,8,9,10\}\) there are computed the minimum distances for 500000 (pairwise nonisometric) binary codes; the table of the distribution of the minimum distances of these codes indicates that the amount of codes with maximum minimal distance is very small.