The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+76x^40+184x^41+378x^42+430x^43+608x^44+898x^45+1111x^46+1328x^47+1557x^48+1736x^49+2004x^50+2172x^51+2432x^52+2524x^53+2407x^54+2544x^55+2159x^56+1940x^57+1606x^58+1308x^59+1024x^60+764x^61+562x^62+358x^63+298x^64+130x^65+112x^66+50x^67+32x^68+14x^69+7x^70+2x^71+5x^72+2x^73+4x^74+1x^78

The gray image is a linear code over GF(2) with n=106, k=15 and d=40.
This code was found by Heurico 1.11 in 42.4 seconds.