The generator matrix

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

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+46x^21+136x^22+276x^23+386x^24+638x^25+906x^26+1074x^27+1249x^28+1122x^29+906x^30+642x^31+387x^32+234x^33+94x^34+54x^35+22x^36+8x^37+6x^38+2x^39+2x^40+1x^44

The gray image is a linear code over GF(2) with n=112, k=13 and d=42.
This code was found by Heurico 1.16 in 1.27 seconds.