The generator matrix

 1  0  1  1
 0  1  3  6

generates a code of length 4 over Z8 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+20x^3+21x^4+20x^5+2x^6

The gray image is a code over GF(2) with n=16, k=6 and d=6.
This code was found by Heurico 1.16 in 4.51e-005 seconds.