I agree with telling them the truth in a little more diplomatic way. Companies have different takes on ethics. They certainly love the concept on the broad level and dealing with the public. Often ethics has a way of being manipulated in reality. So you need to cautiously mention that you did not get the support of management in strengthening the quality standards and implementation of the manual.

tell them the you are looking for a different type of qualities in a company

Tell them the truth.

I wouldn’t use the word quit, ever in an interview situation. It sounds like you just said to heck with you, which maybe you did, but let them find that out IF they call your old employer.
I’d probably clean up the truth a bit and say something like:
I left my last position because communication between departments was lacking and I wanted to find an opportunity where my skills in (fill in the blank with an applicable job description) would be more fully utilized in a team environment where everyone is interested in providing a high quality product/service.