The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+104x^24+54x^25+240x^26+128x^27+1032x^28+384x^29+100x^30+42x^31+24x^32+70x^33+6x^34+2x^39

The gray image is a linear code over GF(3) with n=126, k=7 and d=72.
This code was found by Heurico 1.16 in 0.00473 seconds.