The generator matrix

 1  0  1  1  1  1
 0  1  3  0  0  0
 0  0  4  0  0  0
 0  0  0  4  0  0
 0  0  0  0  4  0
 0  0  0  0  0  4

generates a code of length 6 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+18x^2+63x^4+192x^5+476x^6+192x^7+63x^8+18x^10+1x^12

The gray image is a code over GF(2) with n=24, k=10 and d=4.
This code was found by Heurico 1.16 in 0.000343 seconds.