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.