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  0  0  X  X  0  X
 0  0  X  0  0  0  0  0  0  0 2X  X  X 2X
 0  0  0  X  0  0  0  0  0  X 2X  0 2X 2X
 0  0  0  0  X  0  0  0  0 2X 2X  0 2X  X
 0  0  0  0  0  X  0  0  0 2X 2X  X 2X  0
 0  0  0  0  0  0  X  0  0 2X 2X 2X  X  0
 0  0  0  0  0  0  0  X  0 2X  X 2X  0  0
 0  0  0  0  0  0  0  0  X 2X  0 2X  X  X

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+80x^12+290x^15+768x^18+1758x^21+3216x^24+4238x^27+39366x^28+4182x^30+3066x^33+1554x^36+460x^39+70x^42

The gray image is a linear code over GF(3) with n=42, k=10 and d=12.
This code was found by Heurico 1.16 in 1.88 seconds.