Let A be the 8 X 12 array over Z3 X Z2 X Z2 X Z2 below.  

The first 12 columns of our (24,8,1)-difference matrix are the columns
of A; the other 12 are obtained by adding the following vector to the
columns of A:
   
     (0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111)^T .
   
   
     A: 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
        0000 0010 0100 0110 1000 1010 1100 1110 2000 2010 2100 2110
        0000 0011 1001 2110 0111 2011 2111 1000 0100 1100 1101 2010
        0000 1010 1011 2000 1101 2110 0001 0101 2100 2001 0111 1100
        0000 0001 2010 1111 2111 2100 1101 0011 1010 2101 1000 0110
        0000 1000 2001 1011 0100 1100 0110 2101 2111 0010 1111 2011
        0000 1001 0111 2100 2000 0010 1110 2011 1100 1011 0101 2111
        0000 1011 2101 0100 2110 1001 2000 0110 0101 1111 2011 1010