The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+84x^13+126x^14+512x^15+936x^16+1260x^17+3316x^18+5184x^19+7470x^20+15576x^21+15204x^22+19800x^23+30950x^24+20556x^25+19800x^26+19920x^27+9828x^28+4032x^29+1866x^30+696x^31+20x^33+10x^36

The gray image is a linear code over GF(3) with n=36, k=11 and d=13.
This code was found by Heurico 1.16 in 26.7 seconds.