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.