The generator matrix

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

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+58x^20+76x^21+93x^22+198x^23+299x^24+382x^25+588x^26+752x^27+560x^28+376x^29+291x^30+182x^31+95x^32+62x^33+51x^34+20x^35+10x^36+1x^40+1x^42

The gray image is a linear code over GF(2) with n=108, k=12 and d=40.
This code was found by Heurico 1.16 in 0.341 seconds.