The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+62x^41+144x^42+184x^43+249x^44+284x^45+256x^46+250x^47+267x^48+264x^49+252x^50+256x^51+246x^52+284x^53+262x^54+200x^55+210x^56+158x^57+99x^58+64x^59+49x^60+32x^61+10x^62+6x^63+2x^64+4x^65+1x^74

The gray image is a linear code over GF(2) with n=100, k=12 and d=41.
This code was found by Heurico 1.16 in 1.57 seconds.