Examples of non-formal closed $(k-1)$-connected manifolds of dimensions $\ge 4k-1$

We construct closed $(k-1)$-connected manifolds of dimensions $\ge 4k-1$ that possess non-trivial rational Massey triple products. We also construct examples of manifolds $M$ such that all the cup-products of elements of $H^k(M)$ vanish, while the group $H^{3k-1}(M;\mathbb{Q} )$ is generated by Massey products: such examples are useful for the theory of systols.