So I did try again with a homemade 9:1 UNUN and a 10 m wire to see if I could use it as a simple 14 MHz antenna. But no success… I actually had the best SWR high up on the HF bands.
The toroid is was a T106-2 and what I can see this is not suited for HF UNUNs…
Next I will maybe try one of the SOTA Beam antenna designs (pico-traps, EFHW tuners…).