We designed two 5-qubit gates such that the middle qubit is the target qubit and all four coupled neighbors are the control qubits. These new gates detect the parity between two vertically/horizontally coupled neighbor qubits while cancelling out the coupling effect of horizontally/vertically coupled neighbor qubits. For a 3 by 3 array of 9 qubits with non-tunable couplings, we simulated the effect of our new 5-qubit horizontal and vertical parity detector gates. We achieved the intrinsic fidelity of 99.9% for horizontal and vertical parity detector gates. In this paper we realize Surface Code memories based on the multi-qubit parity detector gates for nearest neighbor superconducting flux qubits with and without tunable couplings. However, our scheme is applicable to other superconducting qubits as well. In our proposed memory realization, error correction cycles can be performed in parallel on several logical qubits or even on the entire 2D array of qubits, this makes it a desirable candidate for large scale and longtime quantum computation. In addition to extensive reduction of the number of control parameters in our method, the error correction cycle time is reduced and does not grow by increasing the number of qubits in the logical qubit layout. Another advantage of this approach is that there will not be any dephasing from idle qubits since all the qubits are used in the error correction cycles.