Is text to code ratio relevant for SEO?

• The short answer is: no. There is no such metric or signal or anything, what would Google measure.
• The long answer is: ...yes! How? Optimizing text to code ratio to the benefit of text, we reduce the code rate. Less code generally effects less page loading time. And this is very well a measurable signal, evaluated by Google and influencing a rank.

So what now? Text to code ration as measurable number isn't relevant for SEO in no way. But it does matter as a first symptom of possible loading time issues, related to dispensable code inside of web document. How to reduce the website code amount?
Disclaimer
The optimization of site loading time isn't a topic of this article, at least cause each site is unique. To get a unique advice about your site loading issues, analyze it with services like GTmetrix, http://gtmetrix.com/: it's free and unifies both of Google's site optimizer and Yahoo's YSlow.
All following advices connote a condition "if possible". Think about this condition and don't adopt each advice blindly!

How to minify the webpage's code length and let searchbots immediately reach your content

 General objectives

1. Mantra number 1: main content loads above the fold;
2. Mantra number 2: "ready to read time" must target 200-300 ms, if page keywords are middle to highly competitive;

 To-do's

• Keep in mind source ordered content: main content comes first!
• No inline CSS-styles;
• No inline JS-javascripts;
• No inline images;
• Put most javascript declarations just before the closing body-tag and not into the HEAD area;
• Just before deploying your project in production stage minify, compress and gzip everything: javascripts, CSS-styles and HTML code. There is a bunch of free and commercial minifying, compressing, gzipping tools, but always test output results - minified/compressed code could get broken, if tools use too aggressive settings.
• Trim protocol from URLs: URLs are still working without "http://";
• Don't close tags, which don't need to be closed (according to HTML version you use);
• Make use of anchors and relative URLs instead of absolute URLs;
• Shorten class and id names;
• Make use of URL shortening services;
• Strip EXIF metadata from images, which you don't self-written.

That's all about code minifying for the moment. Don't neglect the loading time importance, be mindful about details and enjoy the summer!