The generator matrix

 1  0  0  0  0  1  1  1  0  X  1  1  X  X  1  1  1  0  1  X  X  1  1  0  1  X  1  0  0  1  1  X  X  0  1  0  0  1  X  0  1  0  X  0  1  0  1  1  1  1
 0  1  0  0  0  X  X  X  X  1  1  1  1  1 X+1  1 X+1  1  1  0  1  0  1  1  X  X  0  X  1  0 X+1  1  X  X X+1  1  0  X  1  0  X  0  0  0 X+1  1  1 X+1 X+1 X+1
 0  0  1  0  0  0  0  X  0  0  X  X  0  X  X  0 X+1  1  1  1 X+1  1 X+1 X+1 X+1  X  1  1  1 X+1  1  1  1  1  X  X  X  1 X+1  0  X  1  1  0  0 X+1  1 X+1  X  1
 0  0  0  1  0  0 X+1 X+1  1  X  0  1  1  1  X  1  1  X  0  0 X+1  X  X  0  X  1 X+1  1 X+1  0 X+1 X+1  1 X+1  1  0  1  X  X  X  X X+1 X+1  1 X+1 X+1 X+1 X+1  0  1
 0  0  0  0  1  1 X+1  X X+1 X+1  1  0  X  1  0  1 X+1 X+1  X X+1 X+1  0  1  X X+1  0 X+1  0  0  X  X X+1 X+1 X+1  1 X+1  0 X+1  X  1  1  1 X+1  X X+1 X+1  0  1  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+115x^44+222x^46+186x^48+128x^50+97x^52+100x^54+87x^56+46x^58+16x^60+12x^62+10x^64+2x^66+2x^70

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 0.11 seconds.