I'm sure you haven't measured the DC resistance of your inductor
correctly.
Using the same ohmmeter, short the leads together while in ohms mode
and see if you don't get about .2 ohms. That is the resistance of the
ohmmeter leads. The actual resistance of your inductor should be much
less, perhaps around .02 ohms.
I have an inductor with a similar core and similar dimensions. I
don't know for sure that the ferrite material is the same, but it's
probably similar. Looking at the photo of your core, I estimate it's
wound with about 18 gauge wire, about 12 turns per layer.
I rewound my core with 18 gauge wire and about 2 1/2 layers to get
about 20 uH inductance.
I then used an impedance analyzer to measure and plot the AC
resistance of the inductor over the frequency range 100 Hz to 1 MHz.
This resistance is the combination of the increase in wire resistance
due to skin and proximity effect and the ferrite losses. It would be
nice to measure the wire loss alone to see how much of the resistance
is due to wire loss and how much due to the ferrite. One way to do
this if several inductors are available is to use a hammer to break
up and remove the ferrite; then the resistance due to wire alone can
be measured. Another way to do this with small inductors like this is
to use a neodymium iron magnet to fully saturate the ferrite; then the
effect is to have an "air core" inductor.
Here is an image of the analyzer scan of the AC resistance of the
inductor.
http://i49.tinypic.com/2cygps4.png
The top curve is the AC resistance with the ferrite core in place. The
bottom curve is the AC resistance with the ferrite "removed" by means
of a magnet saturating the ferrite.
The resistance at low frequency is about .0137 ohms, and this is also
the DC resistance.
At 100 kHz, the AC resistance with the ferrite in place is about .3
ohms. With the ferrite "removed", the AC resistance at 100 kHz is
about .113 ohms; this is the wire resistance alone.
Here's another image showing the AC resistance versus frequency of a
length of 18 gauge wire in 3 different configurations.
http://i45.tinypic.com/2uro5n8.png
The lowest curve is the AC resistance of a straight piece of 18 gauge
wire; its increasing AC resistance with frequency is due to skin
effect only. The next curve up is the AC resistance with the wire
wound into a single layer solenoid with a 1/4 inch ID; now we get some
proximity effect. The top curve is the same length of wire wound into
a 3 layer coil. Notice how the top curve exhibits a change of slope
at about 50 kHz; this is due to the so-called layer effect, or "eddy
current screening", as Snelling calls it.