Is it possible to run the code in external EEPROM
The initials, "EEPROM" stand for "Electrically-Erasable PROM" - and it is perfectly accurate to describe Flash as "Electrically-Erasable PROM"
Many people, however, take "EEPROM" to refer to a particular type of "Electrically-Erasable PROM" device specifically optimised for use in non-volatile data storage applications.
That is why I asked the OP what he means by EEPROM.
common (unclear) usage is to refer to serially accessible non-volatile memory as EEPROM and parallel accessible as flash.
nevertheless, I know of parallel EEPROM and serial Flash.
Erik