The generator matrix

 1  0  0  0  1  1  1  1
 0  1  0  0  2  5  0  4
 0  0  1  0  3  1  1  4
 0  0  0  1  1  2  2  4
 0  0  0  0  4  0  4  0

generates a code of length 8 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+66x^4+274x^5+649x^6+2024x^7+2149x^8+2044x^9+658x^10+264x^11+56x^12+2x^13+5x^14

The gray image is a code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0316 seconds.