Let $\|a_i^j,\ i=1,\dots,k,\ j=1,\dots,n\|$ , $k=[n\theta]$ , $0<\theta<1$ , be a Boolean matrix with mutually independent random elements $a_i^j$ : $$ \mathbf P\{a_i^j=1\}=\pi_i^j,\quad0<\pi_i^j<1. $$We consider the minimum distance$\zeta$of a random linear code with parity-check matrix$\|a_i^j\|$.Theorem 1. {\it Let all$\pi_i^j\in[\delta,1-\delta]$where$\delta$is a fixed positive number. Then {(3)} holds uniformly for$\pi_i^j\in[\delta,1-\delta]$and for$t$subject to} (1), (2).Theorem 2. (3)holds uniformly for$\pi_i^j\in[\delta_n,1-\delta_n]$as$\delta_n\to0$,$\delta_nn/\ln n\to\infty$and for$t$subject to(4), (5).