763836 1066557 113192 1785102 1470060 3077752 114793 3126753 1997137 2603018
alpha = 1

The unimodular matrix found is

-2  0 -3  1  0  0  0 -1 -1  2 
 0 -1  2  2 -1 -1  3 -1  1  1 
-2  0  0 -1  3 -3 -1  2  1  0 
 0  3  2  3  2 -3  1  0  0 -1 
-2  2  2  0 -1  3 -3 -2 -1  0 
 2  2 -2 -5 -2  1  2  1  1  0 
 0  2  0 -2 -4 -1 -1  4 -1  0 
-3  3 -1  2 -2  1  0  1  4 -6 
 0  2 -1  2 -3 -5 -4 -1  5  3 
-1  0  1 -3  1  3  3 -2 -2  2

Multiplier vector [-1,0,1,-3,1,3,3,-2,-2,2] 

length squared 42

Shortest multiplier:

b[10]-b[1]-b[2]-b[3]-b[5]-b[6]+b[9]=

[3,-1,1,2,-1,-2,-2,-2,2,2], lengthsquared = 36