The generator matrix

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

generates a code of length 6 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+5x^4+10x^5+37x^6+4x^7+2x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=24, k=6 and d=8.
This code was found by Heurico 1.16 in 0.000131 seconds.