The generator matrix

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

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+72x^41+142x^42+184x^43+225x^44+250x^45+264x^46+272x^47+308x^48+254x^49+255x^50+276x^51+258x^52+280x^53+228x^54+212x^55+176x^56+136x^57+120x^58+68x^59+53x^60+30x^61+12x^62+12x^63+3x^64+2x^65+3x^66

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 14.4 seconds.