When removing Family Codes, you will first need to mass remove the codes from the families.
After that, you can continue onto Setup--> Database --> Family Codes and click the trashcan icon to delete.
To do the first step, go Setup--> Database --> Mass Coding.
Click Filters and filter in the view of All Families with the specific Family Codes you wish to delete, and then click Run Report.
Once you click Run Report, you families with the selected codes will appear.
Next, click the Tag and the top of the Tag Column to select all your families.
Click on the green button "Mass Code / Remove Selected Records and select the codes you would like to remove from the selected families. Then click the red button "Remove" and confirm by clicking OK.
Once these codes are removed from the selected families, you can now go to Setup--> Database --> Family Codes and remove the Family Codes.
Same process would also apply for Individual Codes.