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.