As commented on by BenAmada:
I think it would be more ideal to create a new widget that does what you're looking for -- rather than modify the TextBox widget. Others have asked to be able to output Google AdSense code or other pieces of Raw HTML into widgets. It never works very well with the TextBox widget.
A new, very simple widget could be created that has a multi-line textbox in it (not tinyMce), and raw HTML would be pasted into the textbox. I know this widget would be perfect for the AdSense and other Ad people, and sounds like it might fit what you're looking for too.
Please try this and let me know if you have made any improvements. It’s simple and not tested extensively and came right out of the TextBox widget, but without tinyMce and simple required mods.