I would think that the game of "Fizzbin" is an appropriate response to this challenge.
The writers who created the fictional character, Captain Kirk, and had him apparently extemporaneously invent a game with complicated rules called "Fizzbin" cannot be considered an unintelligent source for the aforementioned information content. In every case where the origin coded information is known, it is the product of a mind.
You said that intelligence from non-intelligence is not as mysterious (as life from non-life) But there is no naturalistic, physical/chemical process known to science that creates coded information. The examples of animal intelligence that you listed are derivative of the coded information programmed into the animals DNA, which begs the question of the source of the original coded information in the DNA in those animals.
Cordially,