The generator matrix

 1  0  0  0  1  2
 0  1  0  0  1  4
 0  0  1  0  1  0
 0  0  0  1  1  0
 0  0  0  0  2  2
 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+146x^2+640x^3+3375x^4+7040x^5+10364x^6+7040x^7+3375x^8+640x^9+146x^10+1x^12

The gray image is a code over GF(2) with n=24, k=15 and d=4.
This code was found by Heurico 1.16 in 0.194 seconds.