To change the z-index, open the custom CSS section (click the cog icon in the top right, select Advanced, CSS), then paste in something like the example below. I have shown an example of applying this to two tiles in one line, but you can reference just one if you want. The z-index value of 1 I have used was for tiles displaying images on my dashboard. Other tiles that I wanted to appear on top of the image tiles had a higher z-index value, e.g. 10.
#tile-38, #tile-40 {z-index: 1; !important;}