This can be done two ways:

Via Tool #902 Update Membership/Account Reason Codes
Enter the account base and the closed sequence # for the closed membership into the top section, then press Enter.  The bottom section will reveal the existing code; enter a new one and press Enter to save.

TIP: The advantage of this method is that you can also update the reason code that's on the base share account (-000) for this closed membership at the same time.  Remember that some of our dashboards and reports may use the code from the membership record, while others may use the one from the -000 sub-account, so you may wish to keep those codes in synch. 

TIP: This same tool can also be used to modify the reason code on a closed account as well; see the related item below.

Via Tool #888 Update Closed Membership Information
Enter the account base and closed sequence and use Enter to proceed.  In the left-hand column about midway down the page there is a Reason code field you can update manually.  

TIP: Do not confuse this with the Reason field in the right-hand column, just below Deny membership.  That reason code is entered only if that deny flag is checked, and pertains to the reason you do not want this person to open another membership in the future.