The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X
 0  X 2X  0 2X^2+X 2X 2X^2+X  0 2X^2+X X^2 X^2+X X^2 2X^2+X 2X^2+X
 0  0 X^2  0 X^2  0 2X^2 X^2 X^2 2X^2 X^2  0 2X^2  0
 0  0  0 X^2 2X^2 X^2 X^2 2X^2  0 2X^2 X^2 2X^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+216x^24+452x^27+972x^28+468x^30+72x^33+6x^36

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 0.0259 seconds.