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.