You could check the exit status of codeception maybe? Assuming it's well behaved and sets them properly. Something like (untested!) :
#!/bin/bash
cd /path/to/your/app
OUTPUT=`vendor/bin/codecept run 2>&1`
if [ $? ];
then
echo "${OUTPUT}" | mailx -s 'Codeception Failed' you@somewhere.com
fi
You'll possibly need to apt-get install bsd-mailx to get the mailx command if you're on Ubuntu (or possibly 'mailutils' and it'll ask you for the smtp server etc as part of the 'Satellite server' question). Or there's possibly one of these new-fangled SaaS things your could do a curl post request to - I don't hold with such things though ;-)