Semiconductor spin qubits are an attractive quantum computing platform that offers long qubit coherence times and compatibility with existing semiconductor fabrication technology for scale up. Here, we propose a spin-qubit architecture based on spinless multielectron quantum dots that act as low-crosstalk couplers between a two-dimensional arrangement of spin-qubits in a hexagonal lattice. The multielectron couplers are controlled by voltage signals, which mediate fast Heisenberg exchange and thus enable coherent multi-qubit operations. For the proposed architecture, we discuss the implementation of the rotated XZZX surface code and numerically study its performance for a circuit-level noise model. We predict a threshold of 0.18% for the error rate of the entangling gates. We further evaluate the scalability of the proposed architecture and predict the need for 4480 physical qubits per logical qubit with logical error rates of 10^{-12} considering entangling gate fidelities of 99.99%, resulting in a chip size of 2.6 cm^{2} to host 10, 000 logical qubits.