Duo was wrong, I'd say. It would be unusual English, but not totally wrong. Or did you really spell "park" as "parc"? Now, that would be wrong....
Probably because it's an incredibly rare construction, especially between "go" and its prepositional compliment "to the park", although it might just work with a time expression like "these days". My advice as an EFL teacher - stick with the natural position - before the main verb (unless it's "be").