The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+378x^22+162x^23+660x^24+1242x^25+1458x^26+1158x^27+1242x^28+162x^29+42x^30+54x^31+2x^36

The gray image is a linear code over GF(3) with n=117, k=8 and d=66.
This code was found by Heurico 1.16 in 0.0222 seconds.