The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2  0  1  1  X  0  1  X  1 X^2  0  X
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X X^2  0  X  X X^2  0  0 X^2+X  X  0 X^2+X  0  X X^2  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  X  X  X  X  X  0 X^2+X  0  0 X^2+X X^2 X^2+X X^2+X  X  0
 0  0  0 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 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  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  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 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+99x^20+16x^21+208x^22+96x^23+511x^24+240x^25+704x^26+320x^27+794x^28+240x^29+432x^30+96x^31+221x^32+16x^33+64x^34+35x^36+3x^40

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 0.336 seconds.