Let`s define ternary ECC as a code that its codewords can be defined by $ \{ xyz f(y,z) f(x,z) f(x,y) | x,y,z \in \{0,1\}^m \} $ for some function $f$. $f$ returns bitstring of constant length.

Are there any known good error correction codes that are ternary?

Such a family of LDPC codes would be best.

Is there a reason it won't be good(in terms of distance, rate)?

It might be useful in a construction I have. I just wanted to make sure it is not known already before I dive in.

Thanks