The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1 2X^2+X 2X
 0  1 2X^2+2X+1  2 X+1 2X^2+X 2X^2+X+2 2X 2X^2+1  2 X^2+2 2X^2+X+2 X^2+X+2  1  1
 0  0 2X^2  0 X^2 2X^2 X^2  0 X^2 2X^2 X^2  0 2X^2  0 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+170x^27+486x^28+396x^30+972x^31+144x^33+18x^36

The gray image is a linear code over GF(3) with n=135, k=7 and d=81.
This code was found by Heurico 1.16 in 0.509 seconds.