The generator matrix

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

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+396x^22+186x^23+3448x^24+3972x^25+15546x^26+18248x^27+73206x^28+60678x^29+122236x^30+140148x^31+60492x^32+24762x^33+7260x^34+636x^35+180x^36+36x^37+8x^39+2x^42

The gray image is a linear code over GF(3) with n=135, k=12 and d=66.
This code was found by Heurico 1.16 in 78.3 seconds.