selecting with same time date stamp

I have a sql script shown below. The script will set all records (Except the very first one in the query) to a value of 'I###'
if the value contains the characters 'IAEE'. That is  exactly what I want the script to do.
However the script will fail if the very first record (Earliest time date stamp) and another record with 'IAEE' has the same time date
stamp. How can I fix the query so that it will work if two records have the same time date stamp (Namely if two records have the
same date and the earliest time date stamp).
I have scripted that database table and it is included as an attachement.

The query works fine unless their are two records and they both have the very same date. Is their a way to correct the query so that
t
select * from Goop
 
 update t
   set code = 'I###'
   from Goop t
   where t.DateEntered >= ( select min(x.DateEntered) from Goop x  WHERE SUBSTRING(Code,1,1) = 'I') AND SUBSTRING(Code,1,1) = 'I'
tz.txt