The generator matrix

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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+38x^44+58x^45+85x^46+106x^47+90x^48+76x^49+71x^50+86x^51+62x^52+68x^53+57x^54+30x^55+38x^56+44x^57+30x^58+26x^59+20x^60+10x^61+7x^62+8x^63+7x^64+3x^66+3x^70

The gray image is a linear code over GF(2) with n=102, k=10 and d=44.
This code was found by Heurico 1.16 in 0.125 seconds.