The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  1  X  1  1  0  1  1  1 X^2 X^2  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  0  0  X  X X^2 X^2 X^2+X  X X^2+X  0 X^2+X  X X^2 X^2+X  X  0  X X^2
 0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X  0 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2 X^2  0  X X^2  X  0  0
 0  0  0  X  X  0  X X^2+X  0  X  X X^2 X^2 X^2+X X^2+X  X  0  X  X  0 X^2  0  0  X X^2  X X^2+X X^2+X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 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+35x^22+78x^23+114x^24+162x^25+229x^26+294x^27+290x^28+264x^29+210x^30+148x^31+93x^32+50x^33+34x^34+22x^35+14x^36+4x^37+3x^38+2x^39+1x^42

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 0.104 seconds.