The generator matrix

 1  0  0  1  1  1  1
 0  1  0  2  1  0  2
 0  0  1  1  3  3  1
 0  0  0  4  0  4  4
 0  0  0  0  4  4  4

generates a code of length 7 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+90x^4+96x^5+549x^6+576x^7+549x^8+96x^9+90x^10+1x^14

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 0.00212 seconds.