The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  X  0 2X  X 2X 2X
 0  0  X  0  0  0  0  0 2X  X 2X  0  X 2X
 0  0  0  X  0  0  0  X 2X  0  X  X  0 2X
 0  0  0  0  X  0  0 2X  X 2X 2X  X  X  0
 0  0  0  0  0  X  0 2X  X  X  0 2X  X 2X
 0  0  0  0  0  0  X  X  0  X 2X  0 2X  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+182x^18+156x^21+364x^24+364x^27+4374x^28+546x^30+364x^33+182x^36+28x^42

The gray image is a linear code over GF(3) with n=42, k=8 and d=18.
This code was found by Heurico 1.16 in 0.308 seconds.