The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+116x^18+126x^19+606x^20+986x^21+558x^22+2676x^23+3200x^24+1908x^25+7428x^26+6160x^27+7650x^28+10032x^29+6512x^30+2358x^31+5154x^32+2570x^33+522x^34+348x^35+122x^36+8x^39+8x^42

The gray image is a linear code over GF(3) with n=42, k=10 and d=18.
This code was found by Heurico 1.16 in 3.71 seconds.