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  0  X  X  0
 0  0  X  0  0  0  0  0  0  X 2X 2X  0
 0  0  0  X  0  0  0  0  0 2X 2X 2X  0
 0  0  0  0  X  0  0  0  0 2X 2X  X  0
 0  0  0  0  0  X  0  0  0 2X 2X  0  0
 0  0  0  0  0  0  X  0  0 2X  0  X  0
 0  0  0  0  0  0  0  X  0 2X  0 2X  0
 0  0  0  0  0  0  0  0  X  X 2X  X  0

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+60x^9+236x^12+612x^15+1452x^18+2712x^21+3798x^24+39366x^26+4094x^27+3534x^30+2232x^33+792x^36+160x^39

The gray image is a linear code over GF(3) with n=39, k=10 and d=9.
This code was found by Heurico 1.16 in 1.31 seconds.