The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 1 1 1 1 X 1 X 1 X 1 1 X 0 X X X 1 1 0 0 1 1 1 X 0 0 1 0 1 0 0 1 1 0 0 X
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 X+1 1 X+1 1 X+1 X X 1 X+1 1 1 1 X 1 1 1 0 0 1 X+1 X+1 X+1 1 1 1 1 X X X 0 1 1 X 1 1
0 0 1 0 0 0 0 0 X X 1 1 1 X 0 0 X+1 X+1 X+1 1 1 1 1 X X+1 X 1 1 1 X 0 X+1 1 X 1 0 0 1 X+1 X+1 X+1 0 1 X X 1 1 0 X X
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X X+1 X+1 0 0 1 1 X X X 0 1 X+1 0 1 X X+1 1 X+1 1 1 X+1 1 X X+1 1 X 0 X 1 0 0 X+1 1 X 1
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 0 X 1 1 0 X+1 X 1 X+1 X X+1 X+1 X 1 X X 1 X X+1 X+1 0 0 1 0 X+1 0 0 1 1 0 1 X X X+1
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 1 X 0 0 1 X 1 X X+1 1 1 1 0 1 0 0 X+1 0 X+1 0 1 1 0 1 X 1 X+1 X+1 1 X+1 X 1 X+1 X

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+72x^41+145x^42+194x^43+229x^44+252x^45+254x^46+258x^47+251x^48+254x^49+314x^50+286x^51+266x^52+274x^53+256x^54+190x^55+156x^56+142x^57+101x^58+88x^59+56x^60+26x^61+18x^62+8x^63+4x^65+1x^76

The gray image is a linear code over GF(2) with n=100, k=12 and d=41.
This code was found by Heurico 1.10 in 0.594 seconds.