The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1 1 1 1 0 1 X 1 1 1 0 1 1 1 0 1 X 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 X 1 1 X 1 1 0 X 0 1
0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 0 X+1 1 X+1 1 X 0 X+1 1 X+1 0 0 1 1 1 X+1 1 0 X X 1 0 1 1 X 0 1 1 1 X X+1 1 1 X 1 X+1 1 1 1 0 X+1
0 0 X 0 0 0 0 0 0 0 X 0 0 X X X X 0 0 0 0 X X X X 0 X 0 0 0 X X 0 0 0 X X X 0 0 0 X 0 X X 0 X X X 0 0 X X 0 X 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X 0 X X X X X X X X 0 X X X X X X X X X X 0 X X 0 X X 0 X X X X 0 0 0 X X 0 0 X 0
0 0 0 0 X 0 0 0 0 0 X X X X 0 X X X X X 0 X X X 0 X X 0 0 0 0 0 0 X X X 0 0 X X X X 0 X 0 X X X X 0 X 0 0 0 X 0
0 0 0 0 0 X 0 0 X 0 0 X 0 X 0 X 0 X 0 0 0 X X X X 0 0 X 0 X X 0 X X 0 0 X X X X 0 0 0 X 0 X X X 0 X X 0 X 0 0 0
0 0 0 0 0 0 X 0 X X 0 0 X X 0 0 X 0 X 0 X X X X 0 0 X X 0 0 0 0 X X X X 0 X 0 X 0 0 0 0 X 0 0 0 X 0 X X X 0 X 0
0 0 0 0 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X 0 X X X X X X 0 0 0 X 0 X 0 0 0 0 X 0 X 0 0 0 X X 0 0 X X X X 0 0 X
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+37x^48+50x^49+75x^50+52x^51+61x^52+72x^53+72x^54+92x^55+60x^56+68x^57+52x^58+76x^59+71x^60+56x^61+34x^62+36x^63+10x^64+10x^65+13x^66+9x^68+6x^70+4x^72+4x^74+3x^76
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 0.167 seconds.