The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+50x^18+60x^19+216x^20+152x^21+144x^22+270x^23+302x^24+180x^25+432x^26+192x^27+102x^28+54x^29+28x^30+4x^33

The gray image is a linear code over GF(3) with n=36, k=7 and d=18.
This code was found by Heurico 1.13 in 0.00339 seconds.