Unfortunately, no, you cannot fix that. 20110 is the error you you'll get every time you try to connect to the internet in a DS game.
Just recently, Nintendo permanently discontinued all the Wifi services for the DS and Wii games, which means Black 2 and White 2 are not able to use the internet any more. Since the GTS requires an internet connection to work, it is also disabled.
Basically, that leaves X, Y, Omega Ruby and Alpha Sapphire as the only main-series Pokemon games that can use the internet.