The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  X  0  0  0  X  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2 X^2 X^2  X X^2+X X^2+X X^2+X  X X^2  X  0  0 X^2  0 X^2+X X^2+X  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X  X X^2  X X^2  X  X  X  X  0 X^2  0  X  X  0 X^2+X  X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X  0 X^2 X^2 X^2+X  0 X^2+X X^2  0  X  X  X  0  0 X^2 X^2+X  X
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  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+42x^20+68x^21+143x^22+226x^23+330x^24+414x^25+508x^26+630x^27+534x^28+458x^29+318x^30+158x^31+101x^32+82x^33+52x^34+10x^35+16x^36+2x^37+3x^38

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 0.334 seconds.