The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+106x^18+54x^19+264x^20+426x^21+1242x^22+1266x^23+8226x^24+4374x^25+20052x^26+15954x^27+4320x^28+1698x^29+708x^30+216x^31+48x^32+90x^33+4x^36

The gray image is a linear code over GF(3) with n=117, k=10 and d=54.
This code was found by Heurico 1.16 in 0.947 seconds.