Consider the linear code

$A$:

over $F_4,$ where $$ is a root of $1+x+x^{2}in{F}_2[x].$ Let $B$ be the binary code $\{0000,1100,1010,0110\}$

and consider the $F_2-$linear transformation between $F_4$ and $B$ defined by

$$:$0|0000,1|1100,|1010,1+|0110$

Determine all the codewords of the code

$C$:$={}^{**}(A)=\{((c_1),(c_2))$:$(c_1,c_2)inA\}.$