The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1 2X  1  1  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X  1 2X+2  2 2X^2+2X+1 2X^2+2X+1 2X^2+X+2
 0  0 2X^2  0  0  0 2X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0
 0  0  0 X^2  0 X^2 2X^2 X^2 2X^2  0  0 X^2 2X^2  0 X^2
 0  0  0  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+6x^22+30x^23+150x^24+48x^25+384x^26+580x^27+4032x^28+1476x^29+2600x^30+7968x^31+1446x^32+740x^33+96x^34+66x^35+40x^36+10x^39+10x^42

The gray image is a linear code over GF(3) with n=135, k=9 and d=66.
This code was found by Heurico 1.16 in 53.1 seconds.