The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 2X 0 2X^2+X 2X X^2 2X^2+X X^2+2X X^2 X^2+X X^2+2X X^2 0
0 0 X^2 X^2 2X^2 2X^2 2X^2 X^2 0 X^2 0 X^2 0 0
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+6x^24+24x^25+60x^26+8x^27+552x^28+24x^29+6x^30+12x^31+24x^32+4x^33+6x^34+2x^42
The gray image is a linear code over GF(3) with n=126, k=6 and d=72.
This code was found by Heurico 1.16 in 0.00121 seconds.