That's not the problem, the search weight of all that is set to zero.
Anyway, I've done multiple SQL queries to the database and I've come to some conclusions, they aren't has robust as I would like them to be, but they make some sense, so for this example:
61623ABF0113/6162379091/61623CR017
All words are in the spp_search_word database but not in the spp_search_index database (only the first one 61623ABF0113), the fix is changing them too:
61623ABF0113 /6162379091 /61623CR017
Or
61623ABF0113, 6162379091, 61623CR017
It seems PrestaShop indexing doesn't like big words, that's the only explanation I have for this, it works now, that's what matters to me.