The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X
 0 X^2  0 X^2  0 X^2 2X^2 2X^2 2X^2  0  0 X^2 X^2  0 X^2
 0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+22x^27+192x^30+24x^33+4x^36

The gray image is a linear code over GF(3) with n=135, k=5 and d=81.
This code was found by Heurico 1.16 in 0.000645 seconds.