The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  0  1  1  X X^2+X  1  X  1  1  1  1 X^2  1  1  1 X^2+X X^2+X  1
 0  1  0  0  0  1  1  1  X X+1  1 X^2 X+1  1 X^2+X X^2+1  1 X^2+X+1 X^2+X X^2+X+1 X^2+X+1 X^2+X  0 X^2+X  1  0  X  0
 0  0  1  0  1  0 X^2+1  1  1 X^2+X X+1 X^2+X X+1  0  1 X^2+X+1 X^2+X X^2+X X^2+X X^2+1  1  1 X^2 X^2+X+1 X^2+1  0  X  0
 0  0  0  1  1 X^2+1 X^2  1 X^2+X  X  0 X^2+X+1  1  1  1 X^2+X+1 X^2+1  0  0  X X+1 X+1 X^2+X  X X^2+X+1  1  1  1
 0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  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+64x^22+252x^23+511x^24+688x^25+865x^26+1152x^27+1197x^28+1056x^29+923x^30+700x^31+456x^32+208x^33+63x^34+40x^35+11x^36+5x^38

The gray image is a linear code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.11 in 0.344 seconds.