The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 2X^2
 0  0 X^2  0  0  0 X^2 2X^2 2X^2 X^2 2X^2 X^2  0  0  0
 0  0  0 X^2  0  0 2X^2 2X^2 2X^2  0  0 X^2 X^2 2X^2  0
 0  0  0  0 X^2  0 2X^2 X^2 2X^2 X^2  0 2X^2 X^2  0 2X^2
 0  0  0  0  0 X^2 X^2  0 X^2 X^2 2X^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 21.

Homogenous weight enumerator: w(x)=1x^0+64x^21+120x^24+98x^27+486x^28+4522x^30+972x^31+120x^33+126x^36+40x^39+12x^42

The gray image is a linear code over GF(3) with n=135, k=8 and d=63.
This code was found by Heurico 1.16 in 1.31 seconds.