The generator matrix

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

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+201x^44+304x^46+335x^48+282x^50+245x^52+200x^54+195x^56+146x^58+66x^60+60x^62+13x^64

The gray image is a linear code over GF(2) with n=102, k=11 and d=44.
This code was found by Heurico 1.10 in 0.953 seconds.