Thanks to a comment from Peter (one of the few readers of this blog :-) I found the service UptimeRobot.
There are other services offering availability to monitor servers uptime... but most of them expect that a Web server returns a "200" code. As I worked hard to return a "418" code, most software sees my server as an anomaly. I can not use either TCP or ping controls because my router answers instead of the server if it is disconnected.
UptimeRobot service has the particularity to propose to monitor the presence of a keyword. So I can verify the presence of the text "error 418" to control the operation of my server and receive an alert when he is down.