with: characterized or distinguished by; having as a possession, attribute, accouterment; a person with brown hair.
by: I can find nothing comparable. Over the surface of, through the medium of, along, or using as a route: He came by the highway. She arrived by air.
This surprises me as much as it does you.
Covered by/with was helpful.
When referring to a substance that sticks to another, use in or with: covered with blood
Use covered with to indicate an unusual amount of something on top of something else; use covered by to connote a covering so dense that the object being covered is completely obscured from view:
- The mountain was covered with fog.
- The mountain was covered by fog.
It appears that both by and with can be used in your sentence, the favorite being with by a margin.