The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 1 X 0 1 1 1 X 1 0 X 1 1 1 1 0 X 1 0 X X 0 0 1 1 0 1 1 0 1 1 1 0
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 X+1 1 1 1 X 1 0 0 1 1 1 1 X+1 X 1 1 0 X X 1 1 1 X X 1 1 X+1 0 1 0 0 1
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 0 1 0 1 1 X+1 1 X+1 X 1 1 X+1 0 0 1 1 X+1 1 1 1 0 1 1 0 X X 0 1 X+1 0 0 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 0 X 0 X X X 0 0 X X X X X X X X X 0 0 X X X X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 X X X X 0 0 X 0 0 X 0 0 0 X 0 X 0 X 0 X X X X 0 0 X 0 X X 0 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X X X 0 0 0 X X X X X X X X 0 X X 0 0 X 0 X 0 X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X 0 X X 0 0 0 X X X 0 0 0 X X X X 0 0 X 0 X 0 0 0 0 X X 0 X X 0
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X X 0 0 X 0 0 X X 0 X 0 0 X X 0 0 0 0 X 0 X X X 0 0 X X 0 0 X X 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X X X 0 0 0 0 X X 0 X X X 0 0 0 X 0 0 X 0 0 0 X X X 0 0 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+72x^40+62x^41+124x^42+168x^43+216x^44+222x^45+230x^46+272x^47+271x^48+300x^49+278x^50+304x^51+241x^52+300x^53+232x^54+208x^55+162x^56+118x^57+116x^58+72x^59+54x^60+22x^61+34x^62+6x^64+10x^66+1x^68
The gray image is a linear code over GF(2) with n=100, k=12 and d=40.
This code was found by Heurico 1.16 in 1.9 seconds.