There are a number of programs available which will convert g-code to DXF, a common drawing format. If your device does not support DXF directly, there are a number of programs to convert DXF to SVG. I would paste links but a quick search with your favorite search engine should give you useful results. The better conversion programs will allow you to eliminate movement g-code entries, which prevents connections between lines. I did not paste links, as my research shows such variety as to be overwhelming.
This question is a bit of an edge case for what 3D Printing SE covers, but it has to do with topics most closely related to 3D printing.
I've found a plethora of ways to convert SVG (vector graphics) into G-code, but I can't seem to find any way to take a series of G-code movements and convert them into lines as a vector graphic.
Why would I want to do this, you ask?
I have a Silhouette, which can cut paper, or draw on paper, depending on if you insert a knife tool or a pen tool.
I have a polar draw bot (Makelangelo) which doesn't want to behave... the motors keep losing steps when the number of steps/second is low, and thus positioning gets off.
I want to use the drawing algorithms in the Makelangelo software to create drawings using my Silhouette, but the Silhouette wants vector graphics, not G-code.
The simplest way in my mind to do this is to convert G-code generated in the Makelangelo software, convert it to a standard vector format (SVG), and import it into Silhouette's software suite.
Alternately, if there's a way to send G-code directly to my Silhouette and have it work, that'd be a much better solution.