The generator matrix

 1  1  1  1  1  1  1  X  1  X  1  1  1  X  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X^2+X 2X 2X  0 X^2 2X^2+X  0
 0  0 X^2  0  0  0  0 2X^2 2X^2 2X^2 2X^2 2X^2  0 X^2  0
 0  0  0 X^2  0  0 X^2 2X^2 2X^2  0  0 X^2  0 2X^2 2X^2
 0  0  0  0 2X^2  0 2X^2 2X^2 2X^2  0 2X^2  0 X^2 X^2 2X^2
 0  0  0  0  0 X^2 2X^2  0 X^2 X^2 2X^2 2X^2 X^2 2X^2 X^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+90x^21+406x^24+486x^26+1394x^27+1458x^28+1944x^29+6918x^30+2916x^31+1944x^32+1834x^33+234x^36+48x^39+10x^42

The gray image is a linear code over GF(3) with n=135, k=9 and d=63.
This code was found by Heurico 1.16 in 3.1 seconds.