The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  1  1
 0  1  1  2  0  1  2  1  0  0  0  0  0
 0  0 2X  0  0  0  0  0  0  X  X  X  0
 0  0  0  X  0  0  0  0  X 2X 2X 2X  X
 0  0  0  0  X  0  0  0 2X 2X 2X  X 2X
 0  0  0  0  0 2X  0  0 2X 2X  X  0 2X
 0  0  0  0  0  0  X  0 2X  X 2X  X  X
 0  0  0  0  0  0  0  X  X  0  X  0  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+64x^12+276x^15+924x^18+2562x^21+4374x^22+4758x^24+17496x^25+5564x^27+17496x^28+3828x^30+1446x^33+234x^36+26x^39

The gray image is a linear code over GF(3) with n=39, k=10 and d=12.
This code was found by Heurico 1.16 in 1.04 seconds.