The generator matrix

1 0 0 0 0 1 1 1 0 X 1 1 0 1 1 X 1 0 1 1 1 0 X X X 1 0 1 1 0 1 1 0 1 X X 1 X X X 1 X 1 1 1 1 1 0 X 1
0 1 0 0 0 0 0 X 0 0 X X X 0 0 X 1 1 1 X+1 1 1 1 1 1 X+1 1 X X+1 1 X+1 1 X X 1 1 0 1 X 1 0 0 0 X X+1 1 X 0 0 X
0 0 1 0 0 0 1 1 1 X 0 X+1 1 X+1 X 1 X+1 X 1 0 X+1 X+1 X+1 1 0 X 0 0 X X+1 1 X 1 0 X+1 X+1 X 1 1 1 1 1 X+1 X X 0 X+1 1 1 0
0 0 0 1 0 1 X X+1 1 1 0 1 X 0 X+1 1 0 1 1 1 X X+1 X X+1 0 X 1 X+1 X+1 X+1 1 X X+1 X 1 0 0 1 X+1 X X+1 X 1 0 1 1 X X+1 X+1 X
0 0 0 0 1 X 0 0 X 1 X+1 X+1 1 X+1 1 X+1 1 0 1 0 X 1 0 X X+1 X+1 1 X 1 X+1 X X X X+1 1 X+1 X X 0 X+1 X 1 X+1 X+1 1 X+1 1 0 0 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+124x^44+216x^46+188x^48+124x^50+88x^52+86x^54+108x^56+40x^58+30x^60+14x^62+3x^64+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 1.10 in 0.047 seconds.