The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  X  1  X  1  1  1  1  1  X  1  X  1  1  1  1  X  X  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  X  X  X  X  0  X  X  X  0  X  X  X  0  0  X  X  X  X  X  0  X  0  0  0  X  X  X  X  0  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  0  0  0  X  X  0  0  X  0  X  0  X  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  X  X  0  X  X  0  0  0  0  0  X  0  X  0  X  X  X  0  0  0  0  0  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  0  0  X  0  0  X  X  X  0  X  X  X  0  X  X  X  0  0  X  X  0  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  0  X  X  X  X  0  X  X  0  X  X  X  0  X  X  X  0  0  X  0  0  0  X  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  X  X  0  X  0  0  0  X  0  X  0  X  X  X  0  0  0  X  X  0  0  0  0  0  X  X  X  X
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  0  0  X  X  X  X  X  X
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  0  0  X  0  X  0  0  0  X  0  X  X  X  X  X  0  0  0  X  X  0  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+59x^40+4x^42+135x^44+52x^46+206x^48+140x^50+195x^52+60x^54+97x^56+49x^60+20x^64+5x^68+1x^80

The gray image is a linear code over GF(2) with n=100, k=10 and d=40.
This code was found by Heurico 1.16 in 0.178 seconds.