The generator matrix

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

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+60x^18+54x^22+72x^24+216x^25+20x^27+216x^28+90x^33

The gray image is a linear code over GF(3) with n=39, k=6 and d=18.
This code was found by Heurico 1.16 in 0.00166 seconds.