The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  0  0  0  0  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2  X  0 X^2 X^2+X  X X^2+X X^2  X  X X^2 X^2  X  0  X
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0  X X^2  X X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2+X X^2  0 X^2+X  X  X
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X  0  X  0 X^2+X  0  0 X^2+X  0  X X^2 X^2+X  X
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0 X^2+X  X X^2  X X^2+X  X X^2+X X^2+X  X  0  X  0 X^2+X  X X^2+X
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2

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+188x^22+8x^23+341x^24+136x^25+557x^26+368x^27+914x^28+368x^29+585x^30+136x^31+294x^32+8x^33+135x^34+49x^36+7x^38+1x^44

The gray image is a linear code over GF(2) with n=112, k=12 and d=44.
This code was found by Heurico 1.16 in 4.75 seconds.