The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  1  0  1  X  1  1  1  1  0  1  1  1  0  X  1  1  1  1  0  X  1  0  1  0  X  0  1  1  0  1  1  1  1  X  X  1  1  1  X  1
 0  1  1  0  1  1  0  1  1  X X+1  1  0 X+1  1 X+1  0  1 X+1  1  X X+1  0  0  1 X+1  0  X  1  1  X  1  X  0  1  1 X+1  1 X+1  1  1  1  X  0  1  X  0  0  0  1  1 X+1  1  0  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  X  X  X  X  0  0  X  X  X  X  0  0  X  X  X  0  X  X  0  0  0  X  X  0  X  X  0  0  0  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  0  0  X  X  X  X  X  X  0  X  X  X  X  X  0  X  X  X  X  0  0  0  X  0  0  X  X  X  0  0  X  X  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  X  X  0  X  X  X  X  X  0  X  X  X  0  X  0  X  X  X  X  X  X  0  0  X  X  X  X  X  0  X  0  0  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  X  X  X  X  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  X  X  0  0  X  0  0  0  X  0  0  0  0  X  0  X  0  X
 0  0  0  0  0  0  X  0  0  X  0  0  X  X  0  X  X  X  0  X  0  X  X  0  0  0  X  X  0  X  X  0  0  X  X  X  0  0  0  X  0  X  X  0  X  0  0  X  0  0  X  0  X  0  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  X  X  X  0  0  0  X  0  0  X  0  0  X  X  X  X  0  0  0  X  X  0  X  X  X  X  0  0  0  X  0  0  X  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  0  X  X  0  0  0  X  X  X  X  X  X  0  0  X  0  0  X  0  X  0  X  X  X  0  0  0  X  0  0  X  0  X  X  X  X  X  X

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+36x^47+117x^48+52x^49+174x^50+110x^51+68x^52+152x^53+76x^54+152x^55+148x^56+192x^57+159x^58+124x^59+76x^60+104x^61+52x^62+84x^63+85x^64+12x^65+45x^66+6x^67+16x^72+5x^74+1x^80+1x^82

The gray image is a linear code over GF(2) with n=112, k=11 and d=47.
This code was found by Heurico 1.16 in 24.2 seconds.