Almost A Square, But Not Quite

Geometry Level 5

Suppose $$A, B, C$$ and $$D$$ are 4 points in space that lie on the same plane, with $$ABCD$$ being a quadrilateral. There are 2 perpendicular planes $$\Pi_1$$ and $$\Pi_2$$, such that the orthogonal projections of $$ABCD$$ onto these planes form a square of area $$123$$ each. If $$|AB|=12,$$ what is the perimeter of $$ABCD$$ to 1 decimal place?

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