Fetch all published and hidden pages with 200 response code

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I've got this code to fetch all pages:

/** @var PageArray $pages */
        $pages = $this
            ->wire('pages')
            ->find(sprintf(
                'has_parent!=2,id!=2|7,status<%s',
                Page::statusTrash
            ));

With this I fetch all pages except admin, but that includes the 404 page as well. Is there a way to exclude pages like the 404 page from the result? Or maybe loop through the result set to check for the pages response code (without curl that is)?

I want to avoid filtering the 404 page by ID if possible.

[LostKobrakai]

You might want to use this instead of a hardcoded id: $config->http404PageID