The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+288x^21+1007x^22+1684x^23+3368x^24+4892x^25+7695x^26+8280x^27+10455x^28+8892x^29+8157x^30+4792x^31+3250x^32+1588x^33+733x^34+280x^35+141x^36+20x^37+8x^38+4x^39+1x^40

The gray image is a linear code over GF(2) with n=112, k=16 and d=42.
This code was found by Heurico 1.13 in 28.8 seconds.