Receive notification about error on website

Hi,

From time to time, I find some random error on my client's websites after a plugin and theme update.

To make it easier and faster to catch these errors, is there a plugin that can notify me, by email, about code errors ( actually all errors ) on the website? Or is there a script I can make into a plugin that allow me to receive emails with website console errors?

Sincerely,
Mika