Find a grammar for this language
If you do not want a more complicated (non-context-free) grammar, you cannot coordinate the two steps. The trick is to work the other way around: generate the two "side strings" from one central non-terminal and put the $111$ in the end.

Further problems with your grammar are:


you miss $111$,
since your intention is to generate 2 symbols both at the front and at the end, you would add 4 instead of 2 and thus miss every second odd number. 


I propose the grammar
$$[ \{0,1\}, \{S\}, R, S]$$
where $R$ has the rules 
$S\rightarrow 0S0\ |\  1S1\  |\  0S1\  |\  1S0\  |\  111$.