The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  X  X  1 X^2  X  X  X  1  1 X^2  1  X  0  1  1
 0  X  0  0  0  0  0  0 X^2 X^2+X X^2+X  X X^2+X X^2  X  0  X X^2+X  X  X  X X^2 X^2+X X^2+X X^2 X^2+X  0
 0  0  X  0  0  0  X X^2+X X^2+X  X  X  X X^2 X^2 X^2  X  X  0 X^2+X X^2+X  0  0  X  X  0  X  0
 0  0  0  X  0  X  X X^2+X  0 X^2  X X^2+X X^2+X X^2  0  X  0  0  X  0  X  X X^2+X X^2 X^2  0  0
 0  0  0  0  X  X  0 X^2+X  X X^2+X X^2  X X^2+X  X X^2+X  0  0 X^2 X^2+X  X  X  X  0  X  X  X  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  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+69x^18+78x^19+244x^20+302x^21+571x^22+762x^23+1181x^24+1746x^25+1974x^26+2370x^27+2092x^28+1790x^29+1250x^30+826x^31+513x^32+246x^33+213x^34+56x^35+56x^36+12x^37+19x^38+4x^39+9x^40

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 4.86 seconds.