Praise be to Allah the Lord of the Worlds.

The ruling of Sharia on working for a conventional bank depends on the nature of the work itself. If it doesn`t directly facilitate usurious transactions, then it is permissible, although it is more prudent to avoid doing it. However, if it directly facilitates usurious transactions, then it is forbidden because Allah the Almighty says, " Help ye one another in righteousness and piety, but help ye not one another in sin and rancour: fear Allah. for Allah is strict in punishment."{Al-Maidah, 2}.

Since the bank will use the computer network in its various transactions, be they lawful or unlawful, you (Questioner) aren`t to blame for implementing that network. And Allah knows best.