The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 0 1 1 X X X 1 X 0 0 X X 0 1 1 1 1 1 1 1 1 1 0 1 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 X 0 X 1 X X+1 1 1 0 X 1 1 0 1 1 0 X 1 0 0 X+1 X+1 1 X 1 1 X+1 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 0 1 0 X X+1 X+1 X+1 1 1 X+1 X X 0 0 1 X X X 0 1 1 X+1 X X+1 0 0 1 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 X X X+1 X+1 0 X X+1 1 1 1 X+1 1 1 1 1 X+1 1 X 0 X+1 1 X 0 1 0
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 1 0 0 X 0 X 1 0 1 X+1 X 0 X+1 X 1 X+1 X 0 X X+1 0 X+1 X+1 0 X X+1 0 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X 0 X X X X 0 0 X 0 X X 0 0 0 X X 0 0 0 X 0 0 X X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X 0 0 X X 0 0 X X 0 X X X 0 X X 0 X 0 X 0 0 X X 0 X
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X 0 X 0 X 0 X X X 0 0 X
generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+183x^40+504x^42+796x^44+960x^46+1068x^48+1188x^50+1076x^52+980x^54+787x^56+404x^58+174x^60+60x^62+9x^64+1x^68+1x^84
The gray image is a linear code over GF(2) with n=100, k=13 and d=40.
This code was found by Heurico 1.16 in 6.67 seconds.