The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+160x^15+246x^16+918x^17+1122x^18+1074x^19+3348x^20+4170x^21+3882x^22+10206x^23+8020x^24+5694x^25+9612x^26+5528x^27+2058x^28+2160x^29+672x^30+168x^31+10x^33

The gray image is a linear code over GF(3) with n=36, k=10 and d=15.
This code was found by Heurico 1.16 in 4.64 seconds.