The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  X  1
 0  X  0  0  0  0  0  X  X  X  X  X  0
 0  0  X  0  0  0  X 2X 2X  X  X  0  0
 0  0  0  X  0  0 2X 2X  X  0  X 2X  0
 0  0  0  0  X  0 2X  X 2X  X  0 2X  0
 0  0  0  0  0  X  X  0  X  X 2X 2X  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+132x^18+54x^20+132x^21+324x^23+648x^26+110x^27+432x^29+330x^30+24x^39

The gray image is a linear code over GF(3) with n=39, k=7 and d=18.
This code was found by Heurico 1.16 in 0.0146 seconds.