From that Match History link, it's hard to tell anything at first blush since the page seems to be broken (no graph on Match Overview, no info on Player Builds, Champion/Building Kill map not working), so all that there is to go off of is the raw statistics and what's visible in the scoreboard, but I think that does show enough to indicate that the punishment may well have been warranted.
Your team comp consists of Vladimir, Nocturne, Orianna, Volibear (Yourself) and Ashe, and while the Match history page offers no clue as to which roles you all were assigned, I'm going to guess it was Top, Jungle, Mid, Support, and Bottom, respectively. I say this because both Orianna and Vladimir are running Teleport (which tells me that at least one of them likely had Top Lane, and with Vlad being a meta top-laner, it makes sense he'd go there), and that all besides, everyone else's roles but yours add up.
Now, it'd be one thing to do AP/On-hit Volibear (which is fine), Volibear Support (my sister plays it, she doesn't particularly care about the Support meta), but here's where the problems start.
You went 16/17/7 with 281 CS. As a Support.
Meanwhile Ashe (who, from what I can tell, looks like she resorted at some point to intentionally feeding) went 0/10/2 with 23 CS.
While I don't have immediate access to the replay (or much in the way of reliable information from the match, for that matter), that throws up some serious red flags. It looks to me as though you made a point to troll your ADC, stealing CS and basically making them useless for your own satisfaction.
Of course, it's probable that the Ashe started intentionally feeding before you started stealing CS, but given that you got punished, I think it's much more likely that you went out of your way from the gate to ruin the match for Ashe, and that they started intentionally feeding in response. Both you and them deserve punishment, but either way, it would seem as though your 14-day ban is deserved.