The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  0  X  1  1  1  1  0  1  X  1  0  1  0  1  1  1  0  1  X  X  1  0  X  0  X  X  1  X  X  0  1  1  1  1  X  1  1  1  X
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  1  X X+1  1  X  X  1  1  X X+1  1  X  0 X+1  1  1  0  1 X+1  X  1  X  1  1 X+1  0  1  0  1 X+1 X+1 X+1  0  1  1 X+1  X
 0  0  1  0  0  0  1  1  1  1  X  1  0 X+1 X+1 X+1  X X+1  0  0  X X+1  1  1  1  X X+1  X  0 X+1  0  1  1  1 X+1  1  1  1  0  X X+1  1  1  X  0  1  X  0  X  X  1
 0  0  0  1  0  1  1  0  1  0 X+1 X+1  1  X X+1 X+1  X  0  1  1  0  1  0  1  X  0  1 X+1  X  1  1  1  0  X  0 X+1  1  1  X  1  0  0  1  1  1  0  0  X  0  X X+1
 0  0  0  0  1  1  0  1  1  X  0  X  1 X+1 X+1  0 X+1  X  0 X+1  0  1  X  0  0  1 X+1 X+1  1  0  1  1  1 X+1  1  X  0  1  0  X  1  X  0  1  X  0  1  1  0 X+1  1
 0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  X  0  0  X  0  X  0  X  0  0  X  0  X  X  X  X  0  0  X  X  0  0  X  0  0  X  X  X  X  X  X  X  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  X  X  X  0  0  X  X  X  0  0  X  X  X  0  X  0  0  0  X  X  0  0  0  0  X
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  X  0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  X  X  X  0  0  0  X  X  X  X  X  0  0  0  0  X
 0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  X  X  X  0  0  0  0  0  X  0  X  0  X  0  0  0  0  0  X  X  X  X  X  0  X  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+268x^40+662x^42+1184x^44+1646x^46+2041x^48+2364x^50+2355x^52+2148x^54+1718x^56+1126x^58+553x^60+238x^62+68x^64+8x^66+3x^68+1x^92

The gray image is a linear code over GF(2) with n=102, k=14 and d=40.
This code was found by Heurico 1.16 in 50.6 seconds.