Let the plane \( a x + b y + c z + d = 0 \) bisect the line joining the points \( (4, -3, 1) \) and \( (2, 3, -5) \) at the right angles. If \( a, b, c, d \) are integers, then the minimum value of \( (a^2 + b^2 + c^2 + d^2) \) is ____________.
