The generator matrix
1 1 1
0 4 0
0 0 4
generates a code of length 3 over Z8 who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+3x^2+24x^3+3x^4+1x^6
The gray image is a code over GF(2) with n=12, k=5 and d=4.
This code was found by Heurico 1.16 in 3.1e-005 seconds.