The generator matrix

 1  1  1  1  2  2  2
 0  2  0  2  0  4  4
 0  0  2  2  2  2  2
 0  0  0  4  0  4  0
 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+43x^4+32x^5+80x^6+192x^7+95x^8+32x^9+32x^10+5x^12

The gray image is a code over GF(2) with n=28, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000554 seconds.