Java 8 Convert a stream of set to Map

I have written this lambda that is getting values from a map <Code, Message>contained inside an enum MessageKeyRegistry and creating adding to another map with Code as the key and the MessageKeyRegistry as the value.

Map<MessageKey, MessageKeyRegistry> keyMap = new HashMap<>();
    EnumSet.allOf(MessageKeyRegistry.class)
            .forEach(messageKeyRegistry -> messageKeyRegistry.getCodeToMessage().keySet()
                    .forEach(code -> keyMap.put(code, messageKeyRegistry)));

Now I want to satisfy the immutability concept of functional programming and write a lambda that returns an immutable map directly.