The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 1 X 1 1 X 1 1 X 1 1 X 1 X X X X 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X X X 0 0 0 0 X X X X 0 X X 0 X X 0 X X 0 0 0 0 X 0 0 0 X X 0 X 0 X X 0 X 0 0 X X X 0
0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 X X X 0 X X X 0 X X 0 0 0 0 0 0 0 X X 0 X X X X 0 X 0 0 0 0 X 0 X X 0 0 0 0 0
0 0 0 X 0 0 0 0 0 0 X X X 0 X X 0 X X 0 0 0 0 0 0 0 0 X 0 X X 0 X X X 0 X X 0 0 X X 0 X X X 0 0 X 0 X 0 0 0 X 0
0 0 0 0 X 0 0 0 0 0 X 0 X 0 X 0 X 0 X X X 0 0 X 0 X X X X X X X 0 0 0 0 0 0 X X 0 X X X 0 0 0 X 0 0 X X X X X X
0 0 0 0 0 X 0 0 0 X 0 0 X 0 0 X X X X 0 X 0 X X 0 X 0 0 X X X 0 X 0 X X 0 0 0 0 0 0 X X X X X 0 0 X X 0 0 0 0 0
0 0 0 0 0 0 X 0 0 X 0 X 0 X 0 0 0 X 0 0 0 X X X X X 0 0 X 0 X 0 X X 0 0 X X X 0 X 0 0 X 0 X 0 0 0 X X X 0 0 X 0
0 0 0 0 0 0 0 X 0 X X X 0 X 0 X 0 0 X X X 0 0 X X X X 0 0 X 0 0 X 0 0 0 X 0 0 0 X 0 X X 0 0 X X X 0 X 0 0 0 X 0
0 0 0 0 0 0 0 0 X X X 0 0 X X X X X 0 X 0 X 0 X X 0 X 0 X X X 0 X X X X 0 0 X 0 X X X 0 X 0 0 0 0 0 X 0 0 X X 0
generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+163x^48+18x^50+120x^52+120x^54+231x^56+92x^58+99x^60+24x^62+120x^64+2x^66+20x^68+13x^72+1x^92
The gray image is a linear code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in 31 seconds.