The generator matrix

 1  0  1  1  1  0  1  1  X  1  1 X^2+X  X  1  1  1  0  1 X^2+X  1  1  1  1  0  X X^2  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X X^2+1  1 X^2  0 X+1  X  1 X^2+X+1  1 X+1  1 X+1 X^2+X  1  X  1  0
 0  0  X X^2+X  0 X^2+X  X X^2+X  X X^2  0  0  X  0  0  X  0  X X^2 X^2  X X^2 X^2 X^2  X  X  0
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 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 18.

Homogenous weight enumerator: w(x)=1x^0+26x^18+28x^19+137x^20+160x^21+392x^22+716x^23+1227x^24+1884x^25+2318x^26+2612x^27+2290x^28+1900x^29+1264x^30+708x^31+401x^32+148x^33+86x^34+32x^35+37x^36+4x^37+8x^38+3x^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 3.28 seconds.