The generator matrix

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

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+79x^20+232x^21+471x^22+880x^23+1567x^24+2504x^25+3573x^26+4592x^27+4993x^28+4504x^29+3664x^30+2576x^31+1452x^32+920x^33+471x^34+144x^35+100x^36+32x^37+12x^38+1x^46

The gray image is a linear code over GF(2) with n=112, k=15 and d=40.
This code was found by Heurico 1.16 in 12.9 seconds.