To find the perimeter of a square, we use the formula:
\[ \text{Perimeter} = 4 \times \text{side length} \]
Given the side length of the square is \( 3\sqrt{32} \), we can substitute this value into the formula:
\[ \text{Perimeter} = 4 \times (3\sqrt{32}) \]
Calculating this gives:
\[ \text{Perimeter} = 12\sqrt{32} \]
Next, we need to simplify \( \sqrt{32} \):
\[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \]
Now, we can substitute back into the perimeter calculation:
\[ \text{Perimeter} = 12\sqrt{32} = 12 \times 4\sqrt{2} = 48\sqrt{2} \]
Thus, the perimeter of the square is:
\[ \boxed{48\sqrt{2}} \]