The generator matrix

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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+80x^45+122x^46+94x^47+93x^48+86x^49+69x^50+68x^51+67x^52+44x^53+60x^54+52x^55+37x^56+28x^57+26x^58+36x^59+21x^60+12x^61+10x^62+6x^63+1x^64+6x^65+1x^66+4x^68

The gray image is a linear code over GF(2) with n=102, k=10 and d=45.
This code was found by Heurico 1.16 in 47.1 seconds.