Cost codes are on job cost reports, not general ledger reports. And your GL account would have to be a direct expense account to even hit jobs. 

If you run the 2-4 report for that account, you can drill into each transaction and look at the job costs associated.  Or if you make a list of the record numbers, you could use the "in list" option for printing records in 1-3 and check the include job costs option.  Or if you know the vendor, there is a AP job cost audit report in 4-1-2, but its not modifiable and doesn't appear to include cost code so again you would have to drill down into it.  That's about all I can offer.

Is there a way I can create my own custom report that would display the cost codes for a direct expense GL account.

Is there a way I can create my own custom report that would display the cost codes for a direct expense GL account.

I don't think so since they are not related