Popper has lots of books. Maybe The Myth of the Framework is a good choice. As I recall, it has content from lectures he gave to people not already familiar with his philosophy, so those parts are especially clear and accessible.
Proposing an actual moral goal is tricky, because we have to be careful to keep separate the issues of whether there are true moral ideas, and whether my particular idea is true. And very strictly, my idea will not be true. It will have truth to it, but not be perfect. Which may be a confusing concept, because the prevailing epistemology says that knowledge is "justified, true belief" by which it means 100% absolutely, perfectly true. That perspective discounts any possibility of "partial truths" as knowledge. Further, it encourages people to believe they possess (final, certain) truths. But I don't claim to have any of those, nor do I think one can have those.
If you're OK with all that, I can tell you some tentative guesses at moral truths.
Edit: btw you got the title wrong.
Just the second chapter isn't too long, and should help tremendously.
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