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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+140x^15+280x^18+508x^21+1120x^24+1344x^27+13122x^28+1540x^30+868x^33+616x^36+112x^39+32x^42

The gray image is a linear code over GF(3) with n=42, k=9 and d=15.
This code was found by Heurico 1.16 in 4.52 seconds.