The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  1  1  1
 0  1  1  2 2X+1  0  2  1  X  X 2X+1 X+1  X  0
 0  0 2X  0  X  X 2X 2X  X 2X  0 2X  0  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+18x^24+24x^25+30x^26+56x^27+12x^28+12x^29+54x^30+12x^31+12x^32+6x^34+6x^36

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 0.000642 seconds.