  We use modified traces to renormalize Lyubashenko's closed 3-manifold
invariants coming from twist non-degenerate finite unimodular ribbon
categories. Our construction produces new topological invariants which we
upgrade to 2+1-TQFTs under the additional assumption of factorizability. The
resulting functors provide monoidal extensions of Lyubashenko's mapping class
group representations, as discussed in arXiv:2010.14852. This general framework
encompasses important examples of non-semisimple modular categories coming from
the representation theory of quasi-Hopf algebras, which were left out of
previous non-semisimple TQFT constructions.
