The generator matrix

 1  1  1  1  1  1  1  1  1  3  3  1  1  3  1
 0  9 18  0  9 18  0  9 18  9 18  0  9  0 18

generates a code of length 15 over Z27 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+72x^30+6x^33+2x^36

The gray image is a code over GF(3) with n=135, k=4 and d=90.
This code was found by Heurico 1.16 in 0.000551 seconds.