Magic square of squares

It is a open problem to know whether a $3\times 3$ magic square containing only squares exists or not.

We say a square is almost magic if all the sums are equal except for the anti-diagonal

The following square is almost magic: $$\left[\begin{array}{ccc}{174}^2& {381}^2& {138}^2\\ {291}^2& {222}^2& {246}^2\\ {282}^2& 6^2& {339}^2\end{array}\right]$$
What is the first (lexicographic order) almost magic square with all elements squares of numbers $\le 200$

Answer format: comma separated list of the square root of each element
(All values must be distinct)

Exemple: $174,381,138,291,222,246,282,6,339$ // For the above example

[My timing: 25 sec]