The generator matrix

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

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+30x^24+54x^26+20x^27+108x^29+12x^30+6x^33+6x^36+6x^39

The gray image is a linear code over GF(3) with n=42, k=5 and d=24.
This code was found by Heurico 1.16 in 0.000826 seconds.