The full survey is available as an appendix to the article referenced above.
An expanded and updated version of the CQS, which also measures cultural intelligence in domestic diversity contexts as well as one's cultural value orientations on a model derived from Hofstede's research, is available through the Cultural Intelligence Center.
8:16 am 10 August 2019
There are not very many instruments that measure one's motivation towards interacting with other cultures, or that help the learner understand the value of meta-cognition (strategizing). And, after 20+ years as a study abroad advisor, I can tell you that most undergrads don't think much about using their metacognitive skills to succeed in culture-crossing situations. Using the CQS can help them think more deeply about how they think about intercultural success and also about how mindful strategizing is a good professional skill to have!