The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+39x^38+28x^39+127x^40+106x^41+264x^42+256x^43+388x^44+428x^45+422x^46+542x^47+503x^48+668x^49+581x^50+712x^51+567x^52+576x^53+491x^54+400x^55+314x^56+234x^57+186x^58+104x^59+114x^60+36x^61+56x^62+6x^63+30x^64+9x^66+3x^68+1x^72

The gray image is a linear code over GF(2) with n=100, k=13 and d=38.
This code was found by Heurico 1.16 in 6.97 seconds.