The generator matrix
1 0 0 1 1 1 0
0 1 0 1 2 7 1
0 0 1 1 1 0 3
0 0 0 2 0 6 4
0 0 0 0 4 4 0
generates a code of length 7 over Z8 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+125x^4+384x^5+888x^6+1280x^7+923x^8+384x^9+104x^10+7x^12
The gray image is a code over GF(2) with n=28, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00919 seconds.