hook_menu() with a query string parameter?
hook_menu() doesn't handle query parameters, so the behaviour will have to be within a single page callback.

function MYMODULE_generic_page_callback() {
  $query = drupal_get_query_parameters();
  if (empty($query['code'])) {
    return MYMODULE_without_code_page_callback();
  }
  return MYMODULE_with_code_page_callback();
}




If you need dynamic behaviour for some of the other hook_menu() options, many provide a callback option.  For example "title callback" would also let you use a function to change the page title based on the presence of the query parameter in the same manner as the page callback.  

For access control, it's probably better to return MENU_ACCESS_DENIED or MENU_NOT_FOUND from your page callback.  "access callback" will be called when rendering links to the path to determine if the user has access and the link should be shown, so the query parameter will not be available on the page that contains the link.