The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  X  1  1  X  1  X X^2  1  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X  X  0 X^2+X X^2+X X^2  X  0  0 X^2+X  X X^2  0
 0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2+X  0  X  X  0  0 X^2 X^2 X^2+X X^2  X X^2+X  X X^2+X X^2+X X^2+X X^2
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X X^2+X  X  0 X^2+X  X  X X^2+X  X  0 X^2+X X^2 X^2  0 X^2+X X^2  0  0
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  0  X X^2+X  X X^2+X X^2 X^2+X  0 X^2+X X^2+X  0  0  X X^2+X  0 X^2 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+23x^22+78x^23+143x^24+174x^25+243x^26+264x^27+258x^28+288x^29+189x^30+142x^31+95x^32+46x^33+57x^34+28x^35+14x^36+4x^37+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 0.101 seconds.