The generator matrix

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

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+160x^40+244x^42+660x^44+732x^46+1140x^48+1070x^50+1345x^52+1024x^54+913x^56+456x^58+294x^60+52x^62+85x^64+6x^66+5x^68+5x^72

The gray image is a linear code over GF(2) with n=102, k=13 and d=40.
This code was found by Heurico 1.16 in 7.41 seconds.