The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+32x^21+56x^24+44x^27+486x^28+50x^30+32x^33+18x^36+8x^39+2x^42

The gray image is a linear code over GF(3) with n=42, k=6 and d=21.
This code was found by Heurico 1.16 in 0.0208 seconds.