You've received Error Code 20110 because you are using a discontinued feature.
In May last month, Nintendo shut down all Nintendo Wi-Fi features for the Gen IV and Gen V Pokemo games, and they can no longer be used anymore. Unfortunately, it will never open back up.
So now you can't use the features like GTS, but you can do stuff like trading and battling with someone nearby.
Sorry. :/
Hope I helped. :)
Source: Experience