Supposing that goodness in this context means: value, worth, importance.

The way I see it, the concept of goodness is purely a product of human mind.
Since "goodness" is not measurable objectively, it is subjective.

The answer could vary a lot depending on your definition of "goodness", of course. If it is effort taken to create something, you could probably measure that. Or, perhaps, like the other anon said, clarity. Human reaction is measurable, too.
The thing is, however, your definition of "goodness" and the criteria used is still based on subjectivity somewhere down the line. The question is, where exactly? It's based on your values, of course.

OP is asking: "Do you think there are any cases in which certain pieces could be considered objectively better than others and why?"

Taking >>7 anon as an example, he essentially says "if art should communicate, then art should have clarity". If you accept this, then indeed it is a case where one piece of art could be considered better than another one. (not sure if it could be called objective)

Let's suppose you are arguing with someone who believes post-modern art is just as good as renaissance art. The question should be, good for what? If you figure out what they're basing this opinion on, you have a pretty good shot at finding inconsistencies in what they're saying, thus winning/making them look dumb. Whatever it is you wish.

Hollywood would likely prefer to air a movie that sells well, so you could say from their perspective "better art = more popular art".
In an art school the teacher would probably prefer a painting that got the techniques right. A political twitter page would prefer the picture that agrees with their ideology over a "well drawn" one. So on...