I want to create a field that has the last time the account was touched that was not done by a system admin.
By touch, I mean Newest date out of the following: Task Created date, Event created to date, task modified date, event modified date.
This trigger was built for us but doesn’t exclude the System admin as well as doesn’t give us the last day if they created an activity just gives us a modified date.  Not really sure how to fix it/ adjust it. Any help is appreciated. I have never used Apex before.
 
trigger UpdateLastActivityDate4318 on Task (after insert, after update, after delete, after undelete)
{
    Set<Id> accountIds = new Set<id>();
    if(Trigger.isDelete)
    {
        //always get the old for deleted activities
        for(Task t : Trigger.old)
        {
            accountIds.add(t.AccountId);
        }
    }
    else   
    {
        for(Task t : Trigger.new)
        {           
            accountIds.add(t.AccountId);
        }                  
       
    }
   
  List<Account> accounts =           
            [
                SELECT
                  Id,
                    (
                        SELECT
                          Subject,
                            LastModifiedDate
                        FROM Tasks
                        ORDER BY isClosed ASC, LastModifiedDate DESC
                        LIMIT 1
                    ),
                  Last_Activity_Date__c
                FROM Account
                WHERE Id in :accountIds
            ];
   
   
   
    for (Account a : accounts)
    {
   
        system.debug(a);
       
       
        if(a.Tasks.size() > 0)
        {
            system.debug(a.Tasks[0]);
            a.Last_Activity_Date__c = a.Tasks[0].LastModifiedDate;
        }
        else
        {
            a.Last_Activity_Date__c = null;
        }
    }
   
    update accounts;
}
 
}