The generator matrix

 1  0  1  1  1  4  2
 0  1  1  0  3  1  4
 0  0  2  0  0  4  2
 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+109x^4+96x^5+648x^6+320x^7+683x^8+96x^9+88x^10+7x^12

The gray image is a code over GF(2) with n=28, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00258 seconds.