It is almost impossible to completely get rid of snare drum buzz. Electric Roland kits like the TD-12 and TD-20 allow you to turn snare buzz on so when you play the toms and bass there is a slight snare buzz. Roland has this option because there is usually snare buzz on real kits.
There are things you can do to minimize the snare buzz. Placement of snare in relation to the toms is one way, but it is impractical to move the snare too far away. The drums need to be close enough to move quickly from one drum to another.
Another thing to do is to tune the batter and resonant heads of the snare to different pitches (I tune my batter head higher than the resonant, but some drummers do the opposite). By keeping the 2 snare heads out of tune with each other, the snare will not resonate as easily with the toms.
Also, keep both snare drum heads at different pitches than any of your tom heads. I tune both snare heads higher than all my toms, but if you have a small tom (like an 8 inch tom), you might need to tune the snare between 2 toms.
Make sure that the snare heads are tightened evenly around the edges. If the resonant head is loose at one lug and tight at another lug, you will get some strange sounds.
Finally, make sure you have a fresh set of snares on the drum. Snares wear out just like the heads do. The snares will tend to buzz more, especially if they wear out unevenly since you will have a range of different tightness. At least one of the snares will be more likely to buzz.
It can be frustrating trying to control snare buzz since there are so many variables, but I hope this helps.
On the tuning higher or lower issue - you can tune it either higher or lower, just make sure the pitch doesn't match the pitch of the toms.