The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 1 X 0 1 1 1 X 1 0 1 1 X 0 1 0 0 1 1 1 1 X 1 X 1 X X 0 1 1 1 1 1 0 1 0 0 1 X
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 X+1 1 1 1 X 1 0 0 1 X X 1 1 0 1 X X+1 0 1 X+1 1 X+1 X X 1 1 0 X+1 0 0 1 0 0 0 1 1 X+1 X
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 0 1 0 1 1 X+1 1 X+1 X 1 0 1 0 X 1 1 X X+1 1 1 X X 1 0 1 X 1 0 X 0 1 X 1 1 X+1 X+1 X X
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 0 X 0 0 0 X X X X X X X X 0 X X X 0 X 0 X X 0 0 X X 0 X X 0 X
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 X X X X 0 0 X 0 0 0 X X X 0 X X 0 X X X 0 0 X 0 0 0 0 X 0 0 X 0 X X 0 X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X X X X X X X 0 0 0 X X X 0 0 0 0 X X X X X 0 0 0 X X 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X 0 X X 0 0 0 X X 0 X X 0 X X 0 0 0 0 X 0 X 0 X X 0 X 0 0 0 X 0 X X X X 0 X
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X X 0 0 X 0 0 X X 0 X 0 X X 0 0 X 0 0 X X 0 X 0 0 X 0 0 0 X 0 0 X X 0 0 X 0 X
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X X X 0 0 0 0 X X 0 X 0 0 X X X X 0 0 0 X X X X 0 X X 0 X 0 X 0 X 0 0 0 0
generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.
Homogenous weight enumerator: w(x)=1x^0+112x^46+268x^48+398x^50+523x^52+518x^54+524x^56+539x^58+459x^60+361x^62+219x^64+100x^66+41x^68+16x^70+12x^72+3x^74+1x^76+1x^78
The gray image is a linear code over GF(2) with n=112, k=12 and d=46.
This code was found by Heurico 1.16 in 2.15 seconds.