It should have country boundaries and a grid (15 degree graticule preferably) and it may be simple with unprecise coastlines etcetera. Suitable for on a computer screen, not for high quality print. Developing a map with Mathlab is one thing, and making an Illustrator file I have never done. Is it simple?
I have updated the notebook to make the map in SVG. You can now adjust the parameters as you like (the 15° graticule, the colors, etc), then click on the ︙ menu to get the “download svg” option. You should then be able to open the file in an image editor.