diff --git a/cloudpickle/cloudpickle_fast.py b/cloudpickle/cloudpickle_fast.py
index 70b5ecec..99522a7f 100644
--- a/cloudpickle/cloudpickle_fast.py
+++ b/cloudpickle/cloudpickle_fast.py
@@ -244,7 +244,23 @@ def _enum_getstate(obj):
 
 def _code_reduce(obj):
     """codeobject reducer"""
-    if hasattr(obj, "co_linetable"):  # pragma: no branch
+    # If you are not sure about the order of arguments, take a look at help
+    # of the specific type from types, for example:
+    # >>> from types import CodeType
+    # >>> help(CodeType)
+    if hasattr(obj, "co_columntable"):  # pragma: no branch
+        # Python 3.11 and later: there are some new attributes
+        # related to the enhanced exceptions.
+        args = (
+            obj.co_argcount, obj.co_posonlyargcount,
+            obj.co_kwonlyargcount, obj.co_nlocals, obj.co_stacksize,
+            obj.co_flags, obj.co_code, obj.co_consts, obj.co_names,
+            obj.co_varnames, obj.co_filename, obj.co_name, obj.co_qualname,
+            obj.co_firstlineno, obj.co_linetable, obj.co_endlinetable,
+            obj.co_columntable, obj.co_exceptiontable, obj.co_freevars,
+            obj.co_cellvars,
+        )
+    elif hasattr(obj, "co_linetable"):  # pragma: no branch
         # Python 3.10 and later: obj.co_lnotab is deprecated and constructor
         # expects obj.co_linetable instead.
         args = (
diff --git a/tests/cloudpickle_test.py b/tests/cloudpickle_test.py
index 181a859e..c56e7e8c 100644
--- a/tests/cloudpickle_test.py
+++ b/tests/cloudpickle_test.py
@@ -2386,29 +2386,13 @@ def method(self, arg: type_) -> type_:
 
                 def check_annotations(obj, expected_type, expected_type_str):
                     assert obj.__annotations__["attribute"] == expected_type
-                    if sys.version_info >= (3, 11):
-                        # In Python 3.11, type annotations are stored as strings.
-                        # See PEP 563 for more details:
-                        # https://www.python.org/dev/peps/pep-0563/
-                        # Originaly scheduled for 3.10, then postponed.
-                        # See this for more details:
-                        # https://mail.python.org/archives/list/python-dev@python.org/thread/CLVXXPQ2T2LQ5MP2Y53VVQFCXYWQJHKZ/
-                        assert (
-                            obj.method.__annotations__["arg"]
-                            == expected_type_str
-                        )
-                        assert (
-                            obj.method.__annotations__["return"]
-                            == expected_type_str
-                        )
-                    else:
-                        assert (
-                            obj.method.__annotations__["arg"] == expected_type
-                        )
-                        assert (
-                            obj.method.__annotations__["return"]
-                            == expected_type
-                        )
+                    assert (
+                        obj.method.__annotations__["arg"] == expected_type
+                    )
+                    assert (
+                        obj.method.__annotations__["return"]
+                        == expected_type
+                    )
                     return "ok"
 
                 obj = MyClass()
diff --git a/tox.ini b/tox.ini
index e1ae336b..f7d28f0c 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py35, py36, py37, py38, py39, py310, pypy3
+envlist = py35, py36, py37, py38, py39, py310, py311, pypy3
 
 [testenv]
 deps = -rdev-requirements.txt