Are you using a foam disk or a mauradai? I don't recommend using wire with the disk as it damages the slots. I have tried using a #28 gauge wire without success. It was very hard to get an even weave. It may work on a mauradai with plenty of weights. I have used #24 gauge to braid AROUND and had a free pattern for this in my last issue of Kumi Kapers. You can email me for this at: email@example.com
Let me add just a couple of tips for doing wire kumihimo, but there are many more.
(1) When you are weaving wire, you need to use "bundles" (say 6-8 pieces) of very thin wire for each element, as opposed to one wire per element.
(2) You don't push the wire all the way into the slot, you just sort of put the wire bundle on top and slightly into the edge of the slot to use it more as a position marker than anything else.
(3) You use masking tape to secure the bundles, but I'm not sure if the tape goes on the "starting" bundle, or at the end of each bundle of wires that you weave.
(4) When you are finished, you must pull your wire braid through a draw plate using ever-smaller holes. This is what makes the wire braid even and beautiful.
There are several more tips to make beautiful wire kumihimo braids, but I do not know them all. It would be my recommendation to join the WWJ (wire wrapped jewelry) yahoo group, in addition to staying in this group, of course. There are several people over there who have posted pictures of their beautiful work, and will gladly give you any help you need.