No activation code in the reaction to your ticket ?
Already checked your mail ?
If you really can't find it, contact avast again.
I checked the three emails Avast sent in response to my ticket, and there was no activation code. However (and this is the good news)...
I logged in to my account again, but this time on the main page, in the Licenses category, it says: "You have licenses available to use."
Splendid.
I don't know why, but there are four licenses available. They're all for Avast Internet Security, but they have different expiration dates (31/07/2016, 3/08/2016, 9/08/2016, and 17/12/2016).
I'm not going to question it. I'll just happily enter the activation code for 17/12/2016.
Thanks, Eddy, for suggesting I check again.