The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+134x^20+664x^21+1721x^22+3666x^23+6115x^24+9944x^25+14792x^26+18230x^27+19813x^28+18736x^29+15160x^30+10386x^31+6092x^32+3208x^33+1476x^34+610x^35+197x^36+88x^37+35x^38+4x^39

The gray image is a linear code over GF(2) with n=112, k=17 and d=40.
This code was found by Heurico 1.13 in 60.9 seconds.