The generator matrix

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

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+186x^18+216x^21+1458x^22+378x^24+972x^26+1214x^27+10206x^28+3888x^29+10800x^30+20412x^31+3888x^32+1728x^33+2916x^34+762x^36+24x^45

The gray image is a linear code over GF(3) with n=135, k=10 and d=54.
This code was found by Heurico 1.16 in 0.886 seconds.