$p=\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right), A=\left(\begin{array}{cccc}2 & 1 & 3 & 4 \\ 2 & 5 & 5 & 8 \\ 3 & 6 & 10 & 11 \\ 4 & 8 & 12 & 17\end{array}\right)-\frac{1}{30^{2022}}\left(p p^T\right)^{2023}, B=\left(\begin{array}{llll}2 & 1 & 3 & 4 \\ 0 & 2 & 1 & 3 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 2\end{array}\right)$.
(1)、求矩阵 $A$
(2) 、若 $X$ 满足 $X\left(E-B^{-1} A\right)^T B^T=E$, 求矩阵 $X$