Hi Diego,
There is no way to find this directly from the ArcGIS Administrator or License Manager.
You will need to open the Availability tab in ArcGIS Admin or LM, and double click the feature you wish to know the license code for (ArcGIS for Desktop Basic). It will open a new window which will include a Fulfillment ID.
If you send this Fulfillment ID to Esri Support, they will be able to tell you what license code it is associated with.