For $q^5-q^3-q^2-q+1{leq}d{leq}q^5-q^3-q^2$, we prove the non-existence of a $[g_q(6,d),6,d]_q$ code and we give a $[g_q(6,d)+1,6,d]_q$ code by constructing appropriate 0-cycle in the projective space, where $g_q (k,d)={{sum}^{k-1}_{i=0}}{lceil}frac{d}{q^i}{ ceil}$. Consequently, we have the minimum length $n_q(6,d)=g_q(6,d)+1;for;q^5-q^3-q^2-q+1{leq}d{leq}q^5-q^3-q^2;and;q{geq}3$.