The generator matrix
1 0 0 1 1 1 1 1 0 1 1 1
0 1 0 1 0 2 1 2 1 0 2X 0
0 0 1 2 1 2 1 0 2 0 2X+1 0
0 0 0 2X 0 0 0 0 X X 2X 0
0 0 0 0 2X 0 0 X 2X X X 0
0 0 0 0 0 X 0 2X 2X X 2X X
0 0 0 0 0 0 X 2X 2X 2X 0 0
generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+42x^12+54x^14+204x^15+162x^16+540x^17+1392x^18+1296x^19+2160x^20+6198x^21+3888x^22+4320x^23+16098x^24+5184x^25+4320x^26+8120x^27+2592x^28+1728x^29+618x^30+114x^33+18x^36
The gray image is a linear code over GF(3) with n=36, k=10 and d=12.
This code was found by Heurico 1.16 in 1.05 seconds.