There is an artifact, a clay tablet called the Phaistos disc, that was found in Crete with unusual signs on it. The signs have not been deciphered, but they look logographic in that each symbol is easy to recognize as a common object. Some artifacts with similar symbols have been found, but very very few.
I have mostly stopped granting full posts to undeciphered scripts which only have a few known examples, instead finding a way to mention them in passing. However, the glyphs on the Phaistos disc appear to have been pressed into the clay with some sort of seals or stamps. This makes the Phaistos disc perhaps the very first example of movable type printing — 3000 years before Gutenberg’s printing press, and thus intrinsically interesting.
The layout of the Phaistos disc is also unusual. The script is linear, but the line of the text is in a spiral.
NB: There are several scripts that I have or will mark as being developed around 1500BC. Those scripts have been hard to date, and it’s not clear which one came first, so take all these dates with a grain of salt. Partly there are so many scripts around that time because there was just a lot of activity around Greece, Turkey, and the Levant in that time period.
For reference, note that it is around this time period — 1500BC — that the Chinese Oracle Bone script appeared.
UPDATE: Someone asked me if the glyph at the top was a shower head or what. The Linear B experts call it a shield.