The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+66x^24+126x^25+54x^26+78x^27+90x^28+108x^29+54x^30+90x^31+36x^33+18x^34+2x^36+6x^39

The gray image is a linear code over GF(3) with n=42, k=6 and d=24.
This code was found by Heurico 1.16 in 0.00153 seconds.