The generator matrix

 1  0  0  0  1  1
 0  1  0  0  1  0
 0  0  1  0  1  0
 0  0  0  1  1  0
 0  0  0  0  4  0

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

Homogenous weight enumerator: w(x)=1x^0+76x^2+240x^3+775x^4+1680x^5+2648x^6+1680x^7+775x^8+240x^9+76x^10+1x^12

The gray image is a code over GF(2) with n=24, k=13 and d=4.
This code was found by Heurico 1.11 in 0.000326 seconds.