Pretty sure you need the product code for this since the upgrade code identifies a family of products, and not a single one.
Fire up PowerShell and run this command to get a list of installed products with product code:
Get-WmiObject -Class win32_product
Here is a different way to get the output in a tabular format (IdentifyingNumber is ProductCode):
Get-WmiObject Win32_Product | Format-Table IdentifyingNumber, Name, Version
You can also find the product code in the Property table of the compiled MSI using Orca (MSI SDK tool):