It's probably possible to remove that buzz using some kind of galvanic decoupling (DI box), but frankly that would be putting lipstick on a pig. From my experience, 1/8" mic/line inputs on consumer sound cards, especially of laptops and mobile devices, are pretty unsalvageable.
Get a USB audio interface, made by a brand that's at least somewhat recognised in music production. That'll give you proper mic preamps, in a box with AD-converters that are decoupled from all the interference you have in a computer housing. It'll probably also give a more reliable phantom voltage than that supply you've got there.
The market leader in the cheap-but-usable segment in Behringer, whose U-Phoria UM-2 interface might be just right for you. Though Behringer used to be notorious for noisy inputs – hiss, not buzz – until, so it's often said, they bought Midas and took over their preamp designs. (Which are probably not in the U-Phoria though; anyway I think it doesn't have that much to do with design as with production – small integrated-circuit preamps just can't be made low-noise).
For a little more money you can at any rate already get pretty decent quality with something from Presonus, Focusrite or Tascam.
Though it should, I wouldn't guarantee that the microphone will indeed work flawlessly even with a good audio interface. But if you have an interface you will easily be able to replace the mic with a better one at any point later.
