Lattice-based cryptography is one of the most promising schemes for post-quantum cryptography. Among the many lattice-based cryptosystems, FrodoKEM is a well-known key-encapsulation mechanism (KEM) based on (plain) learning with errors (LWE) problems and is advantageous in that the hardness is based on the problem of unstructured lattices. There are many cryptosystems that adopt error-correcting codes (ECCs) to improve performance, such as LAC, ThreeBears, and Round5. However, for lattice-based cryptosystems that do not use ring structures such as FrodoKEM, it is difficult to use ECCs because the number of transmitted symbols is small. In this study, we propose a method to apply ECCs and Gray codes to FrodoKEM by encoding the bits converted from the encrypted symbols. It is shown that the proposed method improves the security level and/or the bandwidth of FrodoKEM, and 192 message bits, 50% more than the original 128 bits, can be transmitted using one of the modified Frodo-640's.