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 \mathbb{F}_2^m \} $ for some function $f$. 

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