The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+30x^41+115x^42+258x^43+503x^44+734x^45+984x^46+1208x^47+1602x^48+1970x^49+2731x^50+3144x^51+3369x^52+4072x^53+4509x^54+4890x^55+4804x^56+4856x^57+4756x^58+4158x^59+3666x^60+3334x^61+2740x^62+2116x^63+1546x^64+1154x^65+887x^66+532x^67+329x^68+212x^69+149x^70+74x^71+42x^72+22x^73+23x^74+4x^75+5x^76+2x^78+5x^80

The gray image is a linear code over GF(2) with n=112, k=16 and d=41.
This code was found by Heurico 1.11 in 177 seconds.