The generator matrix

 1  1  1  1
 0  3  0  3
 0  0  3  6

generates a code of length 4 over Z9 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+12x^6+54x^8+8x^9+6x^12

The gray image is a code over GF(3) with n=12, k=4 and d=6.
This code was found by Heurico 1.16 in 6.1e-005 seconds.