The generator matrix

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

generates a code of length 5 over Z8 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+8x^3+34x^4+48x^5+24x^6+8x^7+5x^8

The gray image is a code over GF(2) with n=20, k=7 and d=6.
This code was found by Heurico 1.16 in 9.3e-005 seconds.