two coupled fluxonium qubits. Projecting the exchange-coupled two-qubit Hamiltonian onto this subspace yields an effective logical Hamiltonian in which the exchange interaction drives XL rotations and the qubit detuning drives ZL rotations. We model correlated two-levelsystem (TLS) noise by using longitudinal stochastic processes with finite memory time and evaluate encoded-gate performance through the average gate fidelity. Within the projected model, positive spatial noise correlation suppresses the differential fluctuation and thereby improves the fidelity of encoded logical gates. We further compare Gaussian Ornstein-Uhlenbeck, Markovian, and randomtelegraph noise models and examine the role of logical dynamical decoupling. These results identify a noise-adapted control mechanism for odd-parity encoded operations in coupled fluxonium devices and motivate future multilevel simulations including leakage and pulse-level constraints.