Hamada ([8]) and Maruta ([17]) proved the minimum length $n_3(6,;d)=g_3(6,;d)+1$ for some ternary codes. In this paper we consider such minimum length problem for $q{geq}4$, and we prove that $n_q(6,;d)=g_q(6,;d)+1$ for $d=q^5-q^3-q^2-2q+e$, $1{leq}e{leq}q$. Combining this result with Theorem A in [4], we have $n_q(6,;d)=g-q(6,;d)+1$ for $q^5-q^3-q^2-2q+1{leq}d{leq}q^5-q^3-q^2$ with $q{geq}4$. Note that $n_q(6,;d)=g_q(6,;d)$ for $q^5-q^3-q^2+1{leq}d{leq}q^5$ by Theorem 1.2.