The generator matrix

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

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+175x^40+508x^42+806x^44+983x^46+1037x^48+1152x^50+1129x^52+988x^54+739x^56+418x^58+200x^60+45x^62+8x^64+2x^66+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 6.74 seconds.