The generator matrix

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

generates a code of length 5 over Z8 who´s minimum homogenous weight is 4.

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

The gray image is a code over GF(2) with n=20, k=7 and d=8.
This code was found by Heurico 1.16 in 0.000257 seconds.