The generator matrix

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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+216x^40+736x^42+1220x^44+1560x^46+2114x^48+2244x^50+2465x^52+2160x^54+1651x^56+1112x^58+578x^60+248x^62+73x^64+4x^66+1x^68+1x^88

The gray image is a linear code over GF(2) with n=102, k=14 and d=40.
This code was found by Heurico 1.10 in 8.5 seconds.