...is to wrap it in a stored procedure created from the administrator account and grant execute privilige to that stored procedure to the various accounts you want. The accounts won't be able to start the Task directly, but they can call a stored proc that will do the chore:

CREATE PROC RunTask As
EXEC msdb..sp_start_job @job_name = 'Test Task'
GO

GRANT EXECUTE ON RunTask TO MyMinions
GO

-- MyMinions then run
EXEC RunTask