The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+76x^22+76x^23+271x^24+320x^25+414x^26+620x^27+555x^28+640x^29+441x^30+324x^31+164x^32+64x^33+85x^34+4x^35+33x^36+7x^38+1x^42

The gray image is a linear code over GF(2) with n=112, k=12 and d=44.
This code was found by Heurico 1.16 in 0.273 seconds.