The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+226x^40+452x^42+752x^44+958x^46+1192x^48+1054x^50+1188x^52+984x^54+747x^56+364x^58+218x^60+26x^62+25x^64+2x^66+1x^68+1x^72+1x^84

The gray image is a linear code over GF(2) with n=100, k=13 and d=40.
This code was found by Heurico 1.16 in 6.85 seconds.