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.