The generator matrix

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

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+199x^44+84x^46+239x^48+74x^50+180x^52+56x^54+106x^56+36x^58+35x^60+4x^62+6x^64+2x^66+2x^68

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 0.384 seconds.