Based on what you've told us, you don't need a self join at all, i.e. you can simply update an employee's manager id directly
UPDATE Employee
SET ManagerID = 2
WHERE emp_code='1111'
etc
However, if you mean that you need to perform the update given only the emp_code of the employee and the emp_code of the manager (i.e. without the Manager's PK), then you can use a subquery (uncorrelated), e.g.
UPDATE Employee
SET ManagerID = (SELECT manager.Emp_Id
FROM Employee manager
WHERE manager.emp_code = '2222') -- Manager's emp_code
WHERE emp_code='1111' -- Employee to update's emp_code
If you then later need to add a query showing the employee and his / her manager (and assuming that the ultimate boss doesn't have a manager), you can do the self join like so:
SELECT emp.emp_code as EmployeeCode, emp.name as EmployeeName,
mgr.emp_code as ManagerEmpCode, mgr.name as ManagerName
FROM Employee emp
LEFT OUTER JOIN Employee mgr
ON emp.ManagerId = mgr.Emp_Id