A Sequential Magic Square

Place nine different digits (from 0-9) into a 3x3 grid, such that the eight sums formed (three rows, three columns, two diagonals) can be arranged as eight sequential numbers.

Source: Original.

Solutions were received from Al Zimmermann, Colin Bown, Claudio Baiocchi, Stephane Higueret, Philippe Fondanaiche, Vinko Marinkovic. All found the two solutions: 
 Sums from 11 to 18:        Sums from 9 to 16:
 
     1  8  6 --> 15              3  1  8 --> 12
     9  7  0 --> 16              9  2  0 --> 11
     4  3  5 --> 12              4  6  5 --> 15
   / |  |  | \                 / |  |  | \
  /  |  |  |  \               /  |  |  |  \ 
17  14 18 11  13            14  16  9 13  10
Interesting to note is that these two solutions are related - simply subtract each entry from 9, then flip the square left-to-right. - KD
Stephane Higueret pointed out the smallest sequential square with positive (and repeated) entries: 
with elements picks from the set (1,2,4,5) ; (1,1,1,1,2,2,4,4,5)
we can form a sequential Magic square

   | 1  2  1 | 4
   | 4  1  4 | 9
   | 1  2  5 | 8
----------------
 3 | 6  5 10 | 7
Mail to Ken