The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+54x^45+120x^46+210x^47+320x^48+334x^49+378x^50+404x^51+421x^52+510x^53+539x^54+542x^55+525x^56+542x^57+533x^58+512x^59+519x^60+450x^61+372x^62+286x^63+207x^64+130x^65+96x^66+92x^67+49x^68+26x^69+9x^70+2x^71+3x^72+2x^73+3x^76+1x^90

The gray image is a linear code over GF(2) with n=112, k=13 and d=45.
This code was found by Heurico 1.16 in 7.93 seconds.