This is desired coupling. While it is a good idea, to have the application and its error manager loosely coupled, there is no reason to separate the application and its error codes, they belong together.
Dependencies:
+-----------------------+
|Application error codes|<------------+
+-----------------------+ |
^ |
| |
+----------+----------+ |
|Application component| |
+----------+----------+ |
| |
v |
+-----------------------+ +-------+-----+
|Error handler interface|<|---+Error handler|
+-----------------------+ +-------------+