The generator matrix

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

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+40x^24+66x^25+510x^26+120x^27+246x^28+996x^29+130x^30+66x^31+6x^32+2x^33+2x^36+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 0.00306 seconds.