The generator matrix

1 0 0 0 0 1 1 1 0 X 1 1 1 1 1 X 1 1 X 1 0 1 1 0 0 1 0 X 1 X 1 X X X 1 1 1 1 1 1 1 0 1 X 1 1 1 1 1 0 1
0 1 0 0 0 0 0 X 0 0 X X 1 X+1 1 1 X+1 0 1 X+1 1 1 1 X X X+1 1 1 X X 1 0 1 1 1 0 X+1 X X+1 X+1 X+1 1 X+1 1 X+1 X X 1 X 1 0
0 0 1 0 0 0 1 1 1 X 0 X X 1 X+1 0 X X+1 X+1 X+1 X 0 X 1 1 1 1 1 X+1 1 X+1 1 1 1 1 1 X X+1 X+1 1 X+1 X+1 X X 0 1 X 0 0 X 0
0 0 0 1 0 1 X X+1 1 1 0 1 0 0 X X+1 1 X+1 X 1 X 0 1 0 X X+1 X+1 1 X+1 X+1 0 X 0 1 X+1 X X+1 X+1 1 1 0 1 X 1 X+1 1 X+1 X+1 X X 0
0 0 0 0 1 X 0 0 X 1 X+1 X+1 0 X X+1 1 1 1 X 0 1 1 X 1 0 X+1 X X+1 X+1 X X 1 0 1 X+1 X 1 0 X X+1 X X X+1 0 1 X X X+1 X 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+37x^44+82x^45+71x^46+86x^47+92x^48+102x^49+96x^50+38x^51+51x^52+66x^53+52x^54+38x^55+39x^56+54x^57+28x^58+26x^59+32x^60+12x^61+9x^62+4x^63+4x^64+4x^65

The gray image is a linear code over GF(2) with n=102, k=10 and d=44.
This code was found by Heurico 1.10 in 0.032 seconds.