) Ions*

We have synthesized and studied a new iridate, Ba₁₃Ir₆O₃₀, with unusual Ir oxidation states: 2/3 Ir⁶⁺(5d³) ions and 1/3 Ir⁵⁺(5d⁴) ions. Its crystal structure features dimers of face-sharing IrO₆ octahedra, and IrO₆ monomers, that are linked via long, zigzag Ir-O-Ba-O-Ir pathways. Nevertheless, Ba₁₃Ir₆O₃₀ exhibits two transitions at T_N1 = 4.7 K and T_N2 = 1.6 K. This magnetic order is accompanied by a huge Sommerfeld coefficient 200 mJ/mole K below T_N2, signaling a coexisting frustrated/disordered state persisting down to at least 0.05 K. This iridate hosts unusually large J_eff=3/2 degrees of freedom, which is enabled by strong spin-orbit interactions (SOI) in the monomers with Ir⁶⁺ ions and a joint effect of molecular orbitals and SOI in the dimers occupied by Ir⁵⁺ and Ir⁶⁺ ions. Features displayed by the magnetization and heat capacity suggest that the combination of covalency, SOI and large effective spins leads to highly frustrated ferrimagnetic ordering, a novelty of this new high-spin iridate.