The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+180x^26+86x^27+54x^28+360x^29+42x^30+6x^33

The gray image is a linear code over GF(3) with n=126, k=6 and d=78.
This code was found by Heurico 1.16 in 0.000658 seconds.