The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  X  1  1  0  1  0  X  X  1  0  0  0  1  1  1  1  1  0  1  1  X  0  1  1  1  X  1  X  1  1  0  X  1  1  X  0  X  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  X  X  0  X X+1  1  1 X+1  1 X+1  1  1  1  1  1  1  1  1  1 X+1  X  1  X  0  1  1  X  0 X+1 X+1  0
 0  0  1  0  0  0  0  0  0  0  0  0  0  X  0  0  X  1  1  1  1  1  1  1 X+1  1  1  1  1  X  X X+1 X+1  0  X  X  0  1  1  1  1 X+1  X  1  1 X+1  0  1  1  0  1  0
 0  0  0  1  0  0  0  0  0  X  X  1  1 X+1 X+1  1  1  0  0 X+1  X  1  0  1  X  0  1  X  1  1  0 X+1  1  0  X  0  X X+1  0  0  X  0 X+1 X+1  1  1  0  X  1  X  1  0
 0  0  0  0  1  0  0  X  1 X+1  1  0  1  1  1 X+1  X  1  1  X  0  1 X+1 X+1  1  0  X X+1 X+1  0 X+1 X+1 X+1  X  1  X  X  1  1  0  1  X  0  1  0  0  1  0  X  X  1  0
 0  0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  0  X X+1 X+1  X  X  1  0 X+1 X+1  X  0  1 X+1  0 X+1  X X+1  1  1  1  0  1  1  1  X  X  0  0 X+1 X+1  1  1 X+1  1  1  X  0
 0  0  0  0  0  0  1  1  X  1  1 X+1  X  1  X  1  X  1 X+1  1  X  X  X  1  0  1 X+1 X+1 X+1  1 X+1  X  1  X  0  X  X X+1  1  X  X  0  0  1  1  0  0  1  1  1  1  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+63x^40+108x^41+250x^42+376x^43+502x^44+554x^45+664x^46+822x^47+881x^48+1006x^49+1096x^50+1188x^51+1214x^52+1268x^53+1130x^54+1080x^55+947x^56+820x^57+731x^58+508x^59+420x^60+302x^61+194x^62+114x^63+68x^64+34x^65+26x^66+8x^67+4x^69+4x^70+1x^90

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 52.6 seconds.