I’m afraid retrieving country codes cannot be done in one search request yet, see MBS-6741.
The only solution so far is to make additional lookup requests with
inc=area-rels until retrieving area’s country.
For example, in your example request, your first result is the place Bikini Test the area of which is La Chaux-de-Fonds. Use its area MBID to make lookup request for parent area:
Then, make a lookup request for the parent area Neuchâtel (with iso-3166-2 code CH-NE):
It returns every part of Neuchâtel and its parent area (
"backward") Switzerland (with iso-3166-1 code CH).