The generator matrix

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

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+62x^12+182x^15+410x^18+932x^21+1364x^24+13122x^26+1498x^27+1190x^30+668x^33+224x^36+30x^39

The gray image is a linear code over GF(3) with n=39, k=9 and d=12.
This code was found by Heurico 1.16 in 0.256 seconds.