The generator matrix

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

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+61x^20+86x^21+155x^22+292x^23+397x^24+604x^25+846x^26+1052x^27+1156x^28+1072x^29+892x^30+636x^31+380x^32+276x^33+146x^34+68x^35+47x^36+10x^37+9x^38+5x^40+1x^48

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 1.49 seconds.