How to add image only to homepage using sidebar widget…

First of all, my site is goldandbluezone.com

I have a small 160×160 banner image that I only want to appear on the homepage. I added it to the sidebar using the Text widget.

Normally I would use the following code:

<?php
if (is_home()) {
?>
BANNER AD CODE GOES HERE
<?php
}
?>

But, that doesn’t seem to work in the text widget.

Then I went into the editor and Sidebar under the Templates and it worked there, but it’s not centered on my sidebar and just ruins the look of the site.

Any idea how to get this image to only stick to the homepage using the sidebar text widget?