Let $C$ be a ternary linear code with check matrix

$H=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 1\\ 0& 1& 1& 1& 0& 2\\ 0& 2& 1& 0& 1& 1\end{array}\right]$

with check bits in positions $2,4,$ and $6.$

A message $m$ is encoded to a codeword $x.$

This message is sent and received as the word $y=201221.$

Assuming that there is at most one error, correct and decode $y$ to find the message $m$ :