The enlightenment of faith IS a gift from God the Holy Spirit through the word. Without this gift, nobody could believe.
But through this gift, anyone can believe. That is why the parable says that it is not the Sower or the seed that is the problem. It is the soil.
And, just to point out using your own words, this is a GIFT from God. A gift is freely given and freely accepted - or refused. But this goes against another tenet of Calvinism - the irresistible grace to the chosen elect. This too is not scriptural, but even Calvinist defenders like yourself are not immune from the truth of scripture.
“The enlightenment of faith IS a gift from God the Holy Spirit through the word. Without this gift, nobody could believe.”
That is exactly right. And while some would teach that faith is a gift given only to the elect, The Bible teaches otherwise: Romans 12:3 insists that God has dealt to every man the measure of faith.
Now, while we might not understand what the measure of faith is I would assert that it is the right amount to be saved if someone chooses to do so. Particularly after hearing the word of God.