How to change scale (not min & maxvalue) on z-axis in surfplot ?

I have a data in a matrix say 600 x 600 large. For my purpose I plot it with surf, and use view (0, 90). I use caxis([minvalue maxvalue]) to limit the axis of the plot.

However, i would like to "change" the scale of the colorbar, not the min-max values. To a more logarithmic look, or if i possibly can choose it manually. Meaning, the majority of the values I want to plot are around 200 - 1000, but the peak value are at 9000.

I tried set (gca, zaxis ...etc ) but it changed the values on the axis. The actual values on the scale and axis should not change.

Thankful for all help I can get!