Question.Is there a $3$-dimensional integer homology sphere whose universal cover is $\mathbb{R}^3$?

I believe the answer is in the positive and I am looking for (precise) references. If not in dimension $3$, I would be happy with higher dimensional examples.

This question is related to my post: Linking topological spheres and also to the post Have examples of non-simple connected higher-dimensions integer homology sphere? (This link was provided by Ian Agol).