Alcohol inhibits CYP3A4, which is responsible for N-demethylating codeine into the inactive norcodeine, so to that effect it just slows the irreversible deactivation of codeine (leaving more room for O-demethylation by CYP2D6, which is what we want).
The article states
Ethanol showed a biphasic effect on CYP2D6 metabolism, increasing initially the CYP2D6 activity with 175% of control up to a concentration of 1.1%, where after ethanol linearly inhibited the CYP2D6 activity.
It does seem like they imply a 1.75 times increase in CYP2D6 activity, however I'm not sure that it translates to 1.75 more morphine, but it's still a significant increase.
However, I'm a heavy codeine user - 1000 mg once a day, every day for the last half a year. I have drunk a little and a lot of alcohol before taking codeine, and I can't even tell for sure if it pharmacologically potentiates it (hard to tell if you're smashed). There is certainly depressant potentiation - which is obvious if you mix 2 downers. But I definitely didn't feel a doubling in codeine effect, which would be drastic at my 1000 mg dose.
E: reading more of the article, it appears that the best induction of 2D6 happened at 1.1% ethanol concentration, and at 0.1% concentration there was no significant increase. Since codeine metabolism happens in the liver, it would mean that to get the best results you'd have to have 1.1% ethanol concentration in the liver cells, which would require at least 1.1% in the blood I guess. I don't think anyone would be conscious to notice any potentiation at that BAC. According to their graph, you'd need at least something like 0.25-0.3% to get a significant effect, but at that level of intoxication you probably wouldn't notice the minimal effect. This explains why ethanol isn't effective at potentiating codeine.
