The generator matrix

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

generates a code of length 49 over Z2[X]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+62x^35+145x^36+378x^37+575x^38+766x^39+1109x^40+1532x^41+1998x^42+2400x^43+3045x^44+3668x^45+4302x^46+4816x^47+4992x^48+5076x^49+5186x^50+5274x^51+4687x^52+3754x^53+3175x^54+2552x^55+1893x^56+1452x^57+978x^58+652x^59+463x^60+248x^61+144x^62+104x^63+45x^64+20x^65+22x^66+12x^67+4x^68+4x^70+2x^71

The gray image is a linear code over GF(2) with n=98, k=16 and d=35.
This code was found by Heurico 1.11 in 145 seconds.