The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+60x^37+184x^38+268x^39+459x^40+640x^41+798x^42+924x^43+1275x^44+1598x^45+1779x^46+2098x^47+2301x^48+2574x^49+2604x^50+2548x^51+2451x^52+2184x^53+1993x^54+1644x^55+1263x^56+1028x^57+684x^58+504x^59+355x^60+206x^61+131x^62+70x^63+80x^64+30x^65+18x^66+8x^67+7x^68+1x^70

The gray image is a linear code over GF(2) with n=100, k=15 and d=37.
This code was found by Heurico 1.16 in 95.3 seconds.