Encoded magic states are essential for universal fault-tolerant quantum computation, but their resource-efficient preparation in high-rate quantum codes remains challenging. To address this limitation, we propose two-layer verification, which combines local verification of independently prepared subblocks with logical verification after their embedding into a target code. This hierarchy detects harmful error patterns, including even-parity logical-eigenvalue flips that are invisible to a collective product check alone. We demonstrate this scheme for a [[21,3,5]] code by constructing a circuit that embeds three verified seven-qubit Steane-code magic states into the target code. Circuit-level simulations of T- and S-state preparation show logical-error suppression consistent with the code distance. These results demonstrate the potential of two-layer verification as a design principle for reliable magic-state preparation in quantum codes encoding multiple logical qubits.