The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+86x^20+96x^21+239x^22+442x^23+615x^24+896x^25+1109x^26+1194x^27+1115x^28+976x^29+609x^30+398x^31+228x^32+80x^33+86x^34+14x^35+3x^36+4x^38+1x^50

The gray image is a linear code over GF(2) with n=108, k=13 and d=40.
This code was found by Heurico 1.16 in 1.2 seconds.