All stabilizer codes have fault tolerant transversal Bell basis measurement, because Bell basis measurement reveals $X_\text{left}X_\text{right} = \pm 1$ and $Z_\text{left}Z_\text{right} = \pm 1$ (by measuring them) which is very similar to how a qubit's worldline satisfies $X_\text{past}X_\text{future}=+1$ and $Z_\text{past}Z_\text{future}=+1$. Relating X and Z between two spacetime locations are core to why a code can store a qubit fault tolerantly, so the transversal Bell basis measurement is fault tolerant for the "same reason" that the code is fault tolerant. It's just that the simultaneous-X-and-Z-relationship is across space instead of across time.
For example, here is fault tolerant transversal Bell measurement of two 5,1,3 codes:
import stim circuit = stim.Circuit(""" QUBIT_COORDS(0, 0) 0 QUBIT_COORDS(0, 1) 1 QUBIT_COORDS(1, 0) 2 QUBIT_COORDS(1, 1) 3 QUBIT_COORDS(2, 0) 4 QUBIT_COORDS(2, 1) 5 QUBIT_COORDS(3, 0) 6 QUBIT_COORDS(3, 1) 7 QUBIT_COORDS(4, 0) 8 QUBIT_COORDS(4, 1) 9 # Logical bell basis values known before noise MPP X0*X2*X4*X6*X8*X1*X3*X5*X7*X9 MPP Z0*Z2*Z4*Z6*Z8*Z1*Z3*Z5*Z7*Z9 TICK # Stabilizers known before noise MPP X0*Z2*Z4*X6 X1*Z3*Z5*X7 MPP X2*Z4*Z6*X8 X3*Z5*Z7*X9 MPP X4*Z6*Z8*X0 X5*Z7*Z9*X1 MPP X6*Z8*Z0*X2 X7*Z9*Z1*X3 TICK # Noise applied. DEPOLARIZE1(0.001) 0 1 2 3 4 5 6 7 8 9 TICK # Noisy transversal XX measurement. MXX(0.001) 0 1 2 3 4 5 6 7 8 9 DEPOLARIZE2(0.001) 0 1 2 3 4 5 6 7 8 9 # Compare original logical XX to logical XX recovered from physical MXXs. OBSERVABLE_INCLUDE(0) rec[-1] rec[-2] rec[-3] rec[-4] rec[-5] rec[-15] TICK # Noisy transversal ZZ measurement. MZZ(0.001) 0 1 2 3 4 5 6 7 8 9 DEPOLARIZE2(0.001) 0 1 2 3 4 5 6 7 8 9 # Compare original logical ZZ to logical ZZ recovered from physical MZZs. OBSERVABLE_INCLUDE(1) rec[-1] rec[-2] rec[-3] rec[-4] rec[-5] rec[-19] # Compare the original stabilizers across the spacelike measurements. DETECTOR(0, 1, 0) rec[-3] rec[-4] rec[-7] rec[-10] rec[-17] rec[-18] DETECTOR(1, 1, 0) rec[-2] rec[-3] rec[-6] rec[-9] rec[-15] rec[-16] DETECTOR(2, 1, 0) rec[-1] rec[-2] rec[-8] rec[-10] rec[-13] rec[-14] DETECTOR(3, 1, 0) rec[-1] rec[-5] rec[-7] rec[-9] rec[-11] rec[-12] """)
err = circuit.search_for_undetectable_logical_errors( dont_explore_edges_with_degree_above=10, dont_explore_edges_increasing_symptom_degree=False, dont_explore_detection_event_sets_with_size_above=10, canonicalize_circuit_errors=True, ) print("Code Distance is ", len(err)) # prints 3
