The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+35x^18+32x^19+137x^20+136x^21+295x^22+476x^23+789x^24+1288x^25+1698x^26+2152x^27+2228x^28+2168x^29+1774x^30+1312x^31+829x^32+472x^33+247x^34+120x^35+97x^36+32x^37+43x^38+4x^39+13x^40+4x^42+2x^44

The gray image is a linear code over GF(2) with n=112, k=14 and d=36.
This code was found by Heurico 1.16 in 4.79 seconds.