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.