Create a BarLegend in 3D Plot using Manipulate?

Questions
,
1

I have 4D data x,y,z, Temperature . It is really hard to make sense of a 4D data that is why want to generate 2D slices using Plot3D and Manipulate.
I would like to have a barlegend for my plots.
I would like to scale the colormap with the value of my function for given z value and legend change as I change the z value.

Manipulate[
 Plot3D[F = 
   z^2 Sin[\[Pi] x] + z^4 Cos[\[Pi] y] + y^6 Cos[2 \[Pi] y], {x, -3, 
   3}, {y, -2, 2}, PerformanceGoal -> "Quality", Mesh -> None, 
  ColorFunction -> Function[{x, y, z}, Hue[z]], 
  PlotLegends -> BarLegend[Hue, {Min[F], Max[F]}]], {z,
   0, 3, 0.1}, ContinuousAction -> False]

if I make the BarLegend[Hue[z]] I dont see the bar at all.

Any ideas?