I believe it's
9 (At worst you will tie with someone for 4th place) or 10 (Guaranteed clean win)
There are 12*4 = 48 votes in total. If you receive 8 or less votes, then there are still at least 40 remaining ones - more than enough for 4 other people get at least 9.
Here's an example on how you can still lose with 8 votes:
Let there be candidates A (you), B, C, D, and E. Assume the remaining candidates are utterly terrible and thus out of the consideration.
2 Juries vote A, B, C, D
2 Juries vote A, B, C, E
2 Juries vote A, B, D, E
2 Juries vote A, C, D, E
The remaining 4 Juries vote B, C, D, E
A (you) get 8 votes, while B, C, D, and E gets 10.
If you got 9 votes, however, there are only 39 votes remaining. Worst case scenario is that 3 other people got 10 votes and someone ties with you for 4th place with 9 votes.
To visualize this, imagine that in the example above one of the last 4 juries decided against voting one of B/C/D/E and voted for you instead. Then there will be 3 people with 10 votes, and you will tie at 9 votes with the person whose vote got taken.
If a clean win is a must, then 10 votes are necessary.