The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+48x^25+10x^26+8x^27+14x^28+36x^29+6x^30+1x^32+4x^33

The gray image is a linear code over GF(2) with n=108, k=7 and d=50.
This code was found by Heurico 1.16 in 0.392 seconds.