The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0  X 2X  0 2X^2+X 2X X^2 2X^2+X X^2+2X X^2 X^2+X X^2+2X X^2  0 2X^2+X
 0  0 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 X^2  0 X^2  0 2X^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+20x^27+132x^28+366x^30+168x^31+10x^33+24x^34+6x^36+2x^42

The gray image is a linear code over GF(3) with n=135, k=6 and d=81.
This code was found by Heurico 1.16 in 0.00147 seconds.