Gtk window set default gives unexpected result

I have an application with two buttons ( open and close ) and I try to set default on button 2 (close button).

I am trying to work with the gtk_window_set_default() and based on the manual before this call I need to do another call of the gtk_widget_set_can_default() function, which I did.

With the help of the gtk_window_activate_default() function I check activate default.

The problem is that, when I hit enter the open button gets pressed and not the close button like I was expected.

I think that I misunderstood this functions.

Here is a demo program:

#include <gtk/gtk.h>

int main ( void )
{
    GtkWidget       *window;
    GtkWidget       *grid;
    GtkWidget       *button1;
    GtkWidget       *button2;

    /// ***
    gtk_init ( NULL, NULL );

    /// ***
    window = gtk_window_new( GTK_WINDOW_TOPLEVEL );

    grid = gtk_grid_new();
    gtk_container_add( GTK_CONTAINER( window ), grid );

    button1 = gtk_button_new_with_label( "Open" );
    g_object_set( button1, "margin", 50, NULL );

    button2 = gtk_button_new_with_label( "Close" );
    gtk_widget_set_name( button2, "close" );

    g_object_set( button2, "margin", 50, NULL );

    GtkWidget *get_default;
    gtk_widget_set_can_default( button2, TRUE );
    gtk_window_set_default( GTK_WINDOW( window ), button2 );

    get_default = gtk_window_get_default_widget( GTK_WINDOW( window ) );
    const gchar *const get_name = gtk_widget_get_name( get_default );

    if ( gtk_window_activate_default ( GTK_WINDOW( window ) ) )
    {
        g_print( "The default windget got Activated\n" );
        g_print( "The default Widget is now %s\n", get_name );
    }

    gtk_grid_attach( GTK_GRID( grid ), button1, 0, 0, 1, 1 );
    gtk_grid_attach( GTK_GRID( grid ), button2, 1, 0, 1, 1 );

    /// *** Show the Window
    ///gtk_widget_show( window );
    gtk_widget_show_all( window );
    gtk_main ();
}

Output:

The default windget got Activated
The default Widget is now close

The close button is indeed de default one, but when I hit enter the Open button gets clicked.
I know that this thing does

gtk_window_set_accept_focus ()

gtk_window_set_focus ()
gtk_window_get_focus ()

But I am not sure how gtk_window_set_default() works.