The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0 2X^2+X  0  X 2X 2X^2+2X 2X  0 2X^2 2X^2+X 2X X^2+2X  0
 0  0  X X^2+2X 2X  X  0 2X^2+X 2X  0 2X^2+X 2X^2+2X X^2 X^2 X^2
 0  0  0 X^2  0 2X^2  0 X^2 2X^2 X^2 X^2 X^2 2X^2  0 2X^2
 0  0  0  0 X^2 X^2 2X^2 X^2 X^2 X^2  0 X^2 X^2  0 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+40x^21+30x^22+72x^23+266x^24+102x^25+234x^26+824x^27+1902x^28+486x^29+10024x^30+3588x^31+468x^32+1010x^33+168x^34+198x^35+210x^36+42x^37+16x^39+2x^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 0.257 seconds.