No. First, there are no “CSS classes”. A class is a markup language (HTML) concept. It may be referred to in CSS, using a class selector, but this is simply a way to refer to elements by their class. Second, tags are markup language concept too, and you cannot create tags or elements in CSS; in CSS, you just refer to elements by their names.
However, if we interpret the question as “can I format some elements in CSS as if they had code elements inside them”, as I think it is, then the answer is “yes, with reservations”.
For the most of it, all that code markup does is that it sets the font face to a browser-dependent monospace font and the font size to a browser-dependent reduced size, though the latter (poorly documented) applies in some contexts and some browsers only. In addition to this, it may e.g. affect automatic translation programs (like Google Translate) so that they do not translate the content, regarding it as being “not in any human language”—this is normally good, but you cannot do that in CSS. And code markup could have other effects too.
Thus, you might use e.g.
td.bordered {
/* put your settings for the border here */
font-family: monospace;
font-size: 90%;
}
But beware that this does not necessarily produce the same effect as the use of code elements. On the other hand, this should not really be an issue: decide on the desired rendering, and implement it in CSS, instead of trying to imitate some assumed default rendering of code.
something.cssand put your style rules in there. for the<code>tag your rule would becode { ...styles go here... }. If you want to use a class instead do it exactly like you did with the<td>tag in your question. Then just make to include your stylesheet with a<link>tag