Let $[n,k,d]$ be a linear code over $\Bbb F_q$ with minimum distance $d$ and number of minimum weight codewords $N_d$.
How many ways can you select codewords $c_1,\dots,c_T$ (assume $T\ll q^k$) such that there are two non-equal codewords in collection at a distance $d$ from each other ($c_i\neq c_j$, $|c_i-c_j|=d$)?
Presumably answer is $2^{\lambda T}$. If so what is correct estimate to $\lambda$?