Let the product of the focal distance of the point \( P(4, 2\sqrt{3}) \) on the hyperbola \( H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) be \( 32 \). Let the length of the conjugate axis of \( H \) be \( p \) and the length of its latus rectum be \( q \). Then \( p^2 + q^2 \) is equal to ________.
