The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 1 0 1 0 1 1 X 1 1 1 1 1 1 1 0 1 1 0 1 1 X 0 1 1 1 0 0 0 1 1 1 0 X 1
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 1 X+1 0 1 0 1 X+1 0 1 1 0 0 0 X+1 X+1 X+1 1 X X+1 1 X+1 1 1 1 0 X 1 1 1 1 X 0 1 1 1 0
0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 X X X 0 0 0 X X X X 0 X X X X 0 X X X X 0 0 0 0 X X 0 0 0 0 X 0 X 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X X X 0 0 X 0 X X 0 0 X 0 X 0 0 X X 0 X 0 0 X 0 0
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 X X X 0 0 X X 0 X X X 0 X 0 X 0 0 0 0 X X X 0 0 0 0 0 X 0 0 0 0
0 0 0 0 0 X 0 0 0 0 0 X 0 X X 0 X X X X X X X 0 X 0 0 0 X X X X X X 0 0 X 0 X 0 X 0 X 0 0 X X 0 0 0
0 0 0 0 0 0 X 0 0 X 0 0 X X 0 X X 0 X X X 0 X 0 X X X 0 0 X X X X 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0
0 0 0 0 0 0 0 X 0 0 X 0 X 0 0 X X 0 0 X X X X 0 0 X 0 X X 0 0 0 X 0 X X 0 X 0 X 0 0 X 0 X 0 X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 X X X 0 X 0 X 0 X X X 0 X X 0 X X 0 X X 0 0 0 X X 0 X 0 X X X X 0 0 0
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+33x^40+24x^41+73x^42+64x^43+100x^44+104x^45+106x^46+152x^47+148x^48+168x^49+142x^50+168x^51+139x^52+152x^53+101x^54+104x^55+63x^56+64x^57+65x^58+24x^59+14x^60+16x^62+9x^64+8x^66+3x^68+1x^70+2x^72
The gray image is a linear code over GF(2) with n=100, k=11 and d=40.
This code was found by Heurico 1.16 in 0.495 seconds.