  Quantum critical points separating weak ferromagnetic and paramagnetic phases
trigger many novel phenomena. Dynamical spin fluctuations not only suppress the
long-range order, but can also lead to unusual transport and even
superconductivity. Combining quantum criticality with topological electronic
properties presents a rare and unique opportunity. Here, by means of ab initio
calculations and magnetic, thermal, and transport measurements, we show that
the orthorhombic CoTe$_2$ is close to ferromagnetism, which appears suppressed
by spin fluctuations. Calculations and transport measurements reveal nodal
Dirac lines, making it a rare combination of proximity to quantum criticality
and Dirac topology.
