  We perform an extended numerical search for practical fermion-to-qubit
encodings with error correcting properties. Ideally, encodings should strike a
balance between a number of the seemingly incompatible attributes, such as
having a high minimum distance, low-weight fermionic logical operators, a small
qubit to fermionic mode ratio and a simple qubit connectivity graph including
ancilla qubits for the measurement of stabilizers. Our strategy consists of a
three-step procedure in which we: first generate encodings with code distances
up to $d\leq4$ by a brute-force enumeration technique; subsequently, we use
these encodings as starting points and apply Clifford deformations to them
which allows us to identify higher-distance codes with $d\leq7$; finally, we
optimize the hardware connectivity graphs of resulting encodings in terms of
the graph thickness and the number of connections per qubit. We report multiple
promising high-distance encodings which significantly improve the weights of
stabilizers and logical operators compared to previously reported alternatives.
