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.