The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+90x^40+120x^41+234x^42+334x^43+478x^44+582x^45+685x^46+794x^47+927x^48+1034x^49+1063x^50+1138x^51+1116x^52+1296x^53+1157x^54+1136x^55+1039x^56+816x^57+741x^58+558x^59+358x^60+218x^61+183x^62+118x^63+68x^64+30x^65+25x^66+18x^67+16x^68+7x^70+3x^72+1x^74

The gray image is a linear code over GF(2) with n=104, k=14 and d=40.
This code was found by Heurico 1.16 in 51 seconds.