I've seen this mainly in criminal contexts, in the sense of something being exaggerated or falsified (drummed up evidence, drummed up charges).
drum up
1. To work to gain or incite something, often interest or support. A noun or pronoun can be used between "drum" and "up." What else can we do to drum up more support for our campaign? I try to drum up enthusiasm for trigonometry, but my students are just not interested.
2. To create or devise something. A noun or pronoun can be used between "drum" and "up." We need to drum up a story before mom gets home and sees the vase we broke.