The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+178x^44+86x^46+287x^48+77x^50+148x^52+54x^54+106x^56+24x^58+42x^60+12x^62+6x^64+3x^66

The gray image is a linear code over GF(2) with n=100, k=10 and d=44.
This code was found by Heurico 1.16 in 0.152 seconds.