The side lengths $a, b, c$ of a triangle $ABC$ are positive integers. Let:

$$T_{n} = (a+b+c)^{2n} - (a-b+c)^{2n} - (a+b-c)^{2n} + (a-b-c)^{2n}$$

for any positive integer $n$. If $\frac{T_{2}}{2T_{1}} = 2023$ and $a > b > c$, determine all possible perimeters of the triangle $ABC$.

Let's think step by step and output the final answer within \boxed{}.
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