The generator matrix

 1  1  1  1  2  2  1
 0  2  0  6  0  4  0
 0  0  4  0  4  4  0
 0  0  0  4  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+7x^4+12x^5+10x^6+72x^7+5x^8+12x^9+6x^10+3x^12

The gray image is a code over GF(2) with n=28, k=7 and d=8.
This code was found by Heurico 1.16 in 0.000188 seconds.