$ L = \{xyyz\in\{0,1,2\}^{*} : y \neq \epsilon \wedge \exists_{a \in \{0,1,2\}} |y|_a \equiv 0 \}$
Slight more formally, we have 
$$ L = \{xyyz : x,y,z\in\{0,1,2\}^{*} \wedge y \neq \epsilon \wedge \exists_{a \in \{0,1,2\}}\,|y|_a = 0  \}$$

Yes, your regular expression is correct. It can be made simpler.

$(0+ 1 + 2) ^ {*} (00 + 11 + 22 + 0101 + 1010 + 0202 + 2020 + 1212 + 2121)(0 + 1 + 2) ^ {*}$