The generator matrix

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

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+44x^37+153x^38+266x^39+450x^40+632x^41+854x^42+1058x^43+1328x^44+1464x^45+1824x^46+2150x^47+2237x^48+2490x^49+2480x^50+2588x^51+2428x^52+2208x^53+1991x^54+1658x^55+1354x^56+1012x^57+728x^58+518x^59+350x^60+184x^61+140x^62+70x^63+38x^64+26x^65+18x^66+12x^67+6x^68+4x^69+4x^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 1.11 in 38.3 seconds.