I somewhat doubt that you weren't provided with chat logs. You should try closing and re-opening the Client to see if they'll show up, but otherwise, you may have to contact Player Support to get the logs. (although Tantram has been known to provide chat logs on request sometimes, though it might be a while, given the time.)
Either way, if you've had no prior warnings before your 14-day ban, then there's really only two possibilities as far as I can tell;
- You used zero-tolerance chat, such as hate speech or encouragements of self-harm.
- You resorted to gameplay toxicity (trolling, griefing, feeding, etc.)
While I'm not wholly certain myself, it looks like it might be the latter, more specifically feeding. Your most recent match before the ban was as Bard, where you went 0/24/1, with at least seven deaths being within the enemy's domain - one of which, for whatever reason, being inside the enemy base, when the only tower your team had claimed was the top lane's forward tower.
On top of this, your item build looks, to say the least, unusual. Boots of Mobility, a Longsword, Aether Wisp, and a Fiendish Codex - you didn't seem to have a Support item at the end of the game (though that could just be a red herring), but I find the Longsword purchase in particular to be odd. (though, that too could be a red herring).
Either way, your most recent match before the ban seems to point to you having intentionally fed, which would also explain the lack of Chat logs, but, without further knowledge (particularly Rioter comments), I can't really say much more on the matter.
Though, I will say, I really doubt that the ban was unfair, given what little I could find.