You already have 11 words: possible wage deliver gossip first party hair antique salute fuel survey miracle, the 12th word is a combination of 1000110 and a 4 bit checksum. [...]
This
1000110 is what I'm looking for.
How to compute from 11 random words? or 12 random words ?
What I'm understanding, is that the 12th word can't be predicted from the 11 first words. I need to choose a random 12th words, compute something, getting the checksum and chose the words that validate my seed ?
You should generate 7 bits of the 12th word, and then put them after the bits for your first 11 words. Take note of the bit string at this point.
After that download the page
https://iancoleman.io/bip39/ and open it on an offline computer, and select the "Show Entropy Details" checkbox. Then there's a box called "Entropy". In that field you need to put your bit string in there but as a hexadecimal number. It will automatically compute the checksum for you, and therefore the final 4 bits of the 12th word and will show you the correct seed phrase for this entropy.
Now that I think of it, the reason I arrived at a different checksum than you is that Ian Coleman's page is computing the SHA256 sum and first bits different from me, the checksum displayed on his page is definitely correct.