SSMS may have been installed as a 32 bit version, doesn't mean that your server is 32 bit.
To check connect to your server via SSMS and run PRINT @@VERSION
You should get a result like this
Microsoft SQL Server 2012 (SP1) - 11.0.3000.0 (X64)
Oct 19 2012 13:38:57
Copyright (c) Microsoft Corporation
Developer Edition (64-bit) on Windows NT 6.1 <X64> (Build 7601: Service Pack 1)
That will tell you if the SQL instance is 32 or 64 bit.