Yes @ 444 (https://http.cat/status/444). That’s indeed the lightest-weight option.

You have an image on your error page, which some crappy bots will download over and over again.

Most bots won’t download subresources (almost none of them do, actually). The HTML page itself is lean (475 bytes); the image is an Easter egg for humans ;-) Moreover, I use a caching CDN (Cloudflare).