Is there a way to setup a "specific device password " for it ?

A

AC Question

I have 2 steps verification configured for my Google account.
For my old Android Phone, I setup a specific device password and it was fine.
I tried to do the same for my new MotoG 2nd Gen 4G, but only my password works.
As I have 2 steps verification, I put my password, few seconds, I got a SMS with the code and put the code, as configuration for the new account asked me.
However, I really do not want to use my password in my mobile phone, as it would be stored in the phone and with all access to it.
Is there a way to use a specific device password for Google Account ?
Thanks in advance