I don't think you can use AMPscript to populate the product code (storing in a different DE) based on a product the customer will select in the Smart Capture form due to this activity comes from the client side while AMPscript is serverside and you can only interact with it on the server side.
I would recommend using an additional step to process the data. In this case, you can use SQL query to populate the corresponding product code to a new data extension.
I put a sample code for this:
SELECT
a.Product,
b.ProducCode
FROM
[Your target DE] as a
INNER JOIN
[Your lookup DE] as b
ON
a.Product = b.Product