The generator matrix

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

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+162x^24+236x^27+252x^30+72x^33+6x^36

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 0.0448 seconds.