Which homology groups of a closed orientable 6-manifold can be isomorphic to $\mathbb{Z}^3$?

Question

List all $i$ for which there is a closed orientable $6$-manifold $M$ with $H_i(M) =\mathbb{Z}\oplus\mathbb{Z}\oplus\mathbb{Z}$.

I am working on an old exam problem and this one stumped me. Progress so far: I can take $Y=\mathbb{T}^3 \times \mathbb{S}^3$ and get the desired group for $i =1,5,2,4$ I think. But this construction I believe gives $H_3(Y)=\mathbb{Z}^2$. What to do in this case?