The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  X  1
 0  1  1  2  0  1  2  1  0  0  0  X  X
 0  0 2X  0  0  0  0  X  X  X 2X 2X 2X
 0  0  0  X  0  0  X 2X 2X  0 2X 2X 2X
 0  0  0  0  X  0 2X 2X  X 2X  0 2X  X
 0  0  0  0  0 2X  X 2X  X  X  X  0  X

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+174x^18+162x^20+324x^21+972x^23+414x^24+1944x^26+548x^27+1296x^29+630x^30+72x^33+6x^36+18x^39

The gray image is a linear code over GF(3) with n=39, k=8 and d=18.
This code was found by Heurico 1.16 in 0.0531 seconds.