The generator matrix

 1  0  1  1  1  1  1
 0  1  3  0  0  0  0
 0  0  4  0  0  0  0
 0  0  0  4  0  0  0
 0  0  0  0  4  0  0
 0  0  0  0  0  4  0
 0  0  0  0  0  0  4

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

Homogenous weight enumerator: w(x)=1x^0+19x^2+81x^4+539x^6+768x^7+539x^8+81x^10+19x^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 0.00154 seconds.