8x12 = 96 sq ft, divided by 40 chickens = 2.4 sq ft per chicken.
Rather tight, I wouldn't do it myself, but if you live somewhere that has a beautiful climate year-round and they will truly spend all day every day *all year* outside it should have a reasonable chance of being ok.
That sounds kinda tight... Myself, I aim for a minimum of 3.5' square/per bird, preferably 4'. The more room you give them the healthier and happier they'll be, and the less you'll have to clean the coop!
If you're mixing standard-size birds with bantams, I'd be inclined to give them plenty of room so that the bantams won't be bullied and picked on...
Are you planning to get dairy cow(s) or goat(s)? I have three milk cows, and one recommendation I'd make is to have plenty of space in that area too. You're going to be spending a fair percentage of your day in their, so you'll want it to be roomy. Besides, you probably wanna keep your Mom happy right?
One thing you MAY consider is to just make it 8 x 12, have only 24-27 chickens or so, and then later build another coop or add on to the one you have. You'll find a million and half uses for keeping multiple flocks. Separating age groups, breeder flocks, quarantine, a broody with chicks, extra roosters, the list goes on and on! Also, if these are your first chickens, I'd recommend starting small. When I got started with chickens, I got too many too fast, and then lost many of them to beginner mistakes. Just my two cents worth.
ETA: I'm dying to know what breeds you've chosen to get!