The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 1 X X^2 1 X^2 1 1 X 0 X 1 0
0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X^2+X X X X^2 X X X^2+X X X^2 0 X^2 0 X X^2 X
0 0 X X 0 X^2+X X 0 X^2 X X 0 X^2 X^2+X X X^2+X X^2+X X^2+X X 0 X^2+X X X X X X^2+X X 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2
0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0
0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0
0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 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+41x^22+80x^23+120x^24+186x^25+219x^26+268x^27+279x^28+246x^29+213x^30+152x^31+98x^32+70x^33+33x^34+12x^35+13x^36+10x^37+6x^38+1x^40
The gray image is a linear code over GF(2) with n=112, k=11 and d=44.
This code was found by Heurico 1.16 in 0.105 seconds.