The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+72x^22+144x^23+44x^24+258x^25+216x^26+92x^27+306x^28+432x^29+90x^30+270x^31+180x^32+8x^33+66x^34+6x^36+2x^42

The gray image is a linear code over GF(3) with n=42, k=7 and d=22.
This code was found by Heurico 1.13 in 0.00513 seconds.