Mid-point of $\left(4,-3,1\right)$ and $\left(2,3,-5\right)$ is $\left(3,0,-2\right)$ which lies on the plane.

Direction ratios of normal vector to the plane are $\left(1,-3,3\right)$

Equation of Plane is $1(x-3)-3(y-0)+3(z+2)=0$

$x-3y+3z+3=0$

${\left(a^2+b^2+c^2+d^2\right)}_{\min }=28$