The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+39x^18+120x^19+220x^20+318x^21+529x^22+828x^23+1236x^24+1692x^25+2028x^26+2220x^27+2100x^28+1768x^29+1326x^30+852x^31+487x^32+292x^33+155x^34+76x^35+48x^36+26x^37+17x^38+4x^40+2x^42

The gray image is a linear code over GF(2) with n=108, k=14 and d=36.
This code was found by Heurico 1.16 in 4.7 seconds.