The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2  X  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X  0 X^2+X X^2 X^2 X^2+X X^2  0 X^2+X X^2+X X^2 X^2 X^2  0  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0 X^2  X  X  X  X  0  0 X^2 X^2+X  X  0 X^2+X  X  0  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X X^2 X^2+X  0  X  0  X X^2+X X^2 X^2+X X^2+X  X  0  X  X  0
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X  X X^2  0 X^2 X^2+X  0  X X^2  0  0 X^2+X  0  X X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  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+52x^20+92x^21+170x^22+232x^23+256x^24+484x^25+890x^26+1220x^27+1384x^28+1256x^29+831x^30+528x^31+311x^32+196x^33+142x^34+68x^35+44x^36+20x^37+14x^38+1x^46

The gray image is a linear code over GF(2) with n=112, k=13 and d=40.
This code was found by Heurico 1.16 in 1.5 seconds.