The generator matrix

 1  0  0  0  0  1
 0  1  0  0  0  1
 0  0  1  0  0  1
 0  0  0  1  0  1
 0  0  0  0  1  1
 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+186x^2+960x^3+5775x^4+14400x^5+22892x^6+14400x^7+5775x^8+960x^9+186x^10+1x^12

The gray image is a code over GF(2) with n=24, k=16 and d=4.
This code was found by Heurico 1.16 in 0.67 seconds.