The generator matrix
1 1 1 1 1 1 1 1 1 X X X X X
0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 0 X^2 0
generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+14x^27+54x^28+6x^30+6x^33
The gray image is a linear code over GF(3) with n=126, k=4 and d=81.
This code was found by Heurico 1.16 in 0.000426 seconds.