The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+103x^36+166x^37+488x^38+548x^39+953x^40+1020x^41+1551x^42+1990x^43+2666x^44+3096x^45+3637x^46+4262x^47+4431x^48+5176x^49+4914x^50+5176x^51+4595x^52+4586x^53+3797x^54+3276x^55+2648x^56+1856x^57+1588x^58+962x^59+832x^60+440x^61+347x^62+154x^63+142x^64+44x^65+58x^66+16x^67+12x^68+3x^70+1x^72+1x^74

The gray image is a linear code over GF(2) with n=100, k=16 and d=36.
This code was found by Heurico 1.11 in 149 seconds.