The generator matrix

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

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+116x^21+186x^22+294x^23+390x^24+354x^25+576x^26+906x^27+738x^28+612x^29+1006x^30+606x^31+408x^32+246x^33+60x^34+54x^35+8x^36

The gray image is a linear code over GF(3) with n=42, k=8 and d=21.
This code was found by Heurico 1.16 in 0.094 seconds.