This is a common request. You want to extend the Recipient delivery logs (broadLogRcp) schema to add a segmentCode attribute.
Then you want to update the Recipients target mapping to store the segmentCode (see below).
Under additional fields you would add an entry with source expression [targetData/@segmentCode] and destination @segmentCode.
The Target mappings are found under Administration > Campaign management.
PS I have been told that the segmentCode will automatically get mapped once you extend the schema without updating the Target mapping. So try that first, but you would need to take this approach to capture other information than the segmentCode.