The generator matrix

 1  0  0  1
 0  1  0 16
 0  0  1 14

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

Homogenous weight enumerator: w(x)=1x^0+144x^4+2028x^6+576x^7+12312x^8+4040x^9+576x^10+6x^12

The gray image is a code over GF(3) with n=36, k=9 and d=12.
This code was found by Heurico 1.16 in 0.008 seconds.