The generator matrix

 1  0  0  1  1  1  2  2
 0  1  0  2  1  3  1  0
 0  0  1  1  3  6  1  0
 0  0  0  4  0  0  0  4
 0  0  0  0  4  0  0  4
 0  0  0  0  0  4  0  4
 0  0  0  0  0  0  4  4

generates a code of length 8 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+84x^4+288x^5+992x^6+1248x^7+2966x^8+1248x^9+992x^10+288x^11+84x^12+1x^16

The gray image is a code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.033 seconds.