I am talking about the passphrase the bitcoin-qt clients asks whenever I want to send bitcoins or create a new receiving address.
If this is not the on for generating a "brain wallet", how can I proceed to create one?
The standard client cannot generate a "deterministic wallet" (the term "brain wallet" generally refers to the generation of a single address via SHA256 of a long pass phrase whereas "deterministic wallet" refers to using a seed and pass phrase to generate a series of addresses).
If you are keen to create such a wallet then you should look into using Armory or Electrum.