At the moment, there is no way to show the Code instead of the Name within the module. With that said, depending on how your module is set up, you may be able to add the Code as a line item "CODE(ITEM(List))" and format the column widths so that you're only showing the Code rather than the Display Name. This is most beneficial when you have the list on rows, and line items on columns. Then you can adjust the column width for the Row Labels to be 6 and expand the column width for the Code line item.
I forgot to mention, you can also show the Code instead of the list name while exporting the module to a csv,txt, xls file. Once you click Data-> Export, there are two tabs. Under Labels, you can select to show the Code and X out of the Name to show the Code only.