You don't want to redirect to another URL if you expect a 404. There is no 404 response code and it's not very common to redirect.

Normal behavior: just show a 404 page on the current URL.

My suggestion:

Change https://github.com/panique/mini3/blob/master/application/Core/Application.php#L55 and https://github.com/panique/mini3/blob/master/application/Core/Application.php#L59 to:

$this->url_controller = new \Mini\Controller\ErrorController();
$this->url_controller->notFound();

And change https://github.com/panique/mini3/blob/master/application/Controller/ErrorController.php#L20 to notFound.

Then I will be able to set a customised error page for a 404. Direct access to /error should be blocked.