Recent development of the magnetic material engineering led to achievement of the systems with a high interfacial Dzyaloshinskii-Moriya interaction (DMI). As a result, the formation of non-collinear magnetic soliton states or nonreciprocal spin wave dynamics is achievable. Typically used materials are based on bi-layers Heavy Metal/Ferromagnet, e.g., Pt/Co. These layers are characterized not only by a strong DMI, but also by the spin pumping effect and the resulting relatively large damping. Here, we show that the considerable interfacial DMI can be also present in bi-layers based on Ru/Co, characterized with low spin pumping effect and low damping. It is therefore a good candidate for the dynamical studies and implementations of chiral DMI. It is demonstrated by theoretical calculations that the value of DMI can be strongly affected and controlled by the strain of the lattice. We show a systematic experimental and theoretical comparison of magnetic material parameters between Pt/Co and Ru/Co bi-layers as a deserving candidate for spintronic and spin-orbitronic applications.