Do you need to execute the external code synchronously? In other words, must the external code start and run to completion before your trigger ends?
If the answer is yes, then I suggest changing your design. You're using triggers incorrectly and making whatever DML operation fires the trigger tremendously slow.
Assuming the answer is no then, you have options to queue up whatever work needs to be done and have that work executed asynchronously. For example, your trigger could create a record in a work-queue table when it needs this external code to run. Some other process (e.g. a scheduled task, SQL Agent, something in your application, SQL Server Broker) can monitor this table for new records and fire off the appropriate calls as needed.