The generator matrix

 1  0  0  1  1  1  2
 0  1  0  2  1  3  1
 0  0  1  1  3  6  1
 0  0  0  4  0  0  4
 0  0  0  0  4  0  4
 0  0  0  0  0  4  4

generates a code of length 7 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+77x^4+672x^5+168x^6+2240x^7+203x^8+672x^9+56x^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 0.00859 seconds.