The generator matrix

 1  1  1  1  2  1  1
 0  2  0  0  2  0  0
 0  0  2  0  2  0  0
 0  0  0  2  2  0  0
 0  0  0  0  4  0  0
 0  0  0  0  0  4  0

generates a code of length 7 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+29x^2+131x^4+607x^6+512x^7+607x^8+131x^10+29x^12+1x^14

The gray image is a code over GF(2) with n=28, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00148 seconds.