We generate multipartite entangled states of two, three and four matter qubits, where the entanglement is distributed over macroscopic distances via a photonic network link. Trapped-ion qubits are entangled directly via the optical fibre link, and the entanglement is subsequently extended to memory qubits co-trapped in each network node, using local mixed-species logic gates. We create remotely entangled - and - states, as well as mixed-species states of up to four qubits. We demonstrate storage of the remotely-entangled memory qubits for $\sim\SI{10}{\second}$, more than $100\times$ the state creation time.