The generator matrix
1 1 1 1 1 1 1 1 1 X X 0 1 1
0 X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X 2X^2+X 2X X 0 X^2
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+54x^26+14x^27+54x^28+108x^29+6x^30+6x^33
The gray image is a linear code over GF(3) with n=126, k=5 and d=78.
This code was found by Heurico 1.16 in 0.000535 seconds.