The generator matrix

 1  1  1  1
 0  9  0  0
 0  0  9  0
 0  0  0  9

generates a code of length 4 over Z27 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+8x^3+24x^6+648x^8+32x^9+16x^12

The gray image is a code over GF(3) with n=36, k=6 and d=9.
This code was found by Heurico 1.16 in 8.61e-005 seconds.