The generator matrix

 1  0  1  1  1
 0  1  1  4  3
 0  0  2  6  4

generates a code of length 5 over Z8 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+16x^3+66x^4+96x^5+56x^6+16x^7+5x^8

The gray image is a code over GF(2) with n=20, k=8 and d=6.
This code was found by Heurico 1.16 in 0.000138 seconds.