The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  1  1 X^2  1  0  1  1  1  0  1  1  1 X^2  1 X^2+X  1  1  X  1
 0  1  1  0 X^2+X+1  1  X  1 X^2+X+1 X^2+X  1  1  X  1  X X+1 X+1  1  X X^2+X  0  1 X^2+1  1 X^2+1 X^2+X  0 X+1
 0  0  X  0 X^2+X  0  0 X^2 X^2  0 X^2  X  X X^2+X  X X^2+X  0  X  X  X  X  0  X X^2+X X^2+X X^2+X X^2+X  X
 0  0  0  X  0  0 X^2+X X^2+X  X X^2  X X^2 X^2  X X^2+X  X  0 X^2  0  X  X  X X^2+X X^2+X X^2+X X^2 X^2  X
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  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+43x^22+140x^23+204x^24+328x^25+487x^26+534x^27+624x^28+602x^29+445x^30+328x^31+171x^32+92x^33+45x^34+22x^35+24x^36+2x^37+4x^38

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 0.27 seconds.