Code details

best found code with parameters
q=3 k=8 n=140
minimum distance = 87

this is new code


the previous bounds were 86/89
this is a projective code


We used the prescribed group of automorphisms with the following generators


1 1 0 0 1 1 2 2
2 2 0 2 2 0 2 1
0 0 2 2 0 2 1 2
2 1 2 1 0 2 0 2
2 0 2 2 1 2 0 2
1 2 0 2 1 1 2 1
1 0 1 0 1 2 1 0
2 2 1 1 0 2 0 1

This group makes 118 orbits of sizes (first row):
The solution (second row) of the corresponding linear system of equations was found after less than 94 seconds:

28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 4 28 28 28 28
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


The second part of the solution :

53 50 44 53 53 41 50 41 41 35 53 44 53 53 44 41 44 44 50 44 53 41 44 50 41 44 50 41 35 35 53 50 53 50 44 44 53 53 41 44 44 50 44 53 53 53 41 53 50 44 41 53 50 44 53 41 32 53 53 53 50 44 35 44 53 53 53 50 44 50 50 44 44 44 44 44 53 53 41 53 44 53 50 50 41 50 44 41 53 44 44 44 50 44 44 44 35 44 50 44 53 50 44 44 53 41 44 53 53 50 41 53 53 41 35 44 41 35


This produces the following generator matrix

0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1 0 0 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1 1 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1
2 2 0 0 0 2 2 2 2 2 0 0 0 2 1 0 0 0 0 1 2 2 2 1 1 1 1 1 0 2 0 0 2 2 1 0 0 0 0 1 0 2 2 1 1 0 0 0 0 0 2 2 1 1 1 1 0 0 2 2 0 0 0 2 2 1 0 2 2 2 1 1 2 2 2 2 1 1 0 0 0 0 2 1 2 2 0 0 2 1 1 1 1 1 0 0 0 2 2 2 1 1 0 2 2 1 1 0 2 2 2 1 0 0 2 0 0 2 1 0 0 0 2 0 0 1 1 1 1 1 0 0 0 0 2 2 1 1 1 1
0 1 0 1 1 0 0 2 2 1 0 2 1 2 2 0 2 2 2 2 2 1 1 0 2 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 2 0 2 0 1 0 0 0 2 1 2 1 0 2 2 1 0 2 0 0 2 2 1 0 1 1 0 0 0 2 0 2 2 2 1 1 0 2 0 0 0 2 0 1 2 1 0 2 0 0 0 2 2 2 0 0 0 1 1 1 1 1 2 0 2 2 1 2 0 0 2 2 2 2 2 2 2 1 1 0 0 1 1 2 1 0 0 0 1 1 0 2 2 2 1 1 0 2 2 2
0 0 1 0 2 0 1 0 1 1 2 1 2 2 0 1 0 2 1 0 0 2 2 0 1 2 2 1 0 2 0 1 0 2 1 2 2 1 1 0 1 1 2 1 2 0 0 1 0 0 2 0 1 0 2 2 2 0 0 2 0 0 1 2 1 1 0 0 1 2 0 1 2 1 2 2 0 2 0 1 1 1 0 2 2 0 1 1 1 2 2 2 1 1 0 2 1 0 2 2 2 1 1 0 1 1 0 2 0 2 0 1 2 1 0 0 2 0 0 2 2 0 0 0 2 0 0 2 0 2 2 0 0 1 2 1 1 0 2 2
2 1 1 1 1 2 2 0 2 0 1 0 1 0 0 1 0 2 0 2 2 0 0 1 2 2 1 0 2 2 2 0 0 1 0 0 1 0 2 0 1 0 1 2 2 0 2 1 2 1 0 0 1 2 2 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 2 1 1 2 0 0 0 1 2 0 1 2 2 0 0 1 1 0 2 0 1 0 1 1 1 1 0 0 0 2 1 2 2 0 1 2 2 0 2 1 1 0 1 1 2 0 1 1 1 0 1 2 1 0 2 2 1 2 0 0 2 0 2 0 0 1 1 1 0 0
2 2 0 1 1 2 1 0 1 1 1 0 1 1 0 2 2 0 0 0 2 2 1 2 2 2 2 1 1 0 2 1 0 2 1 2 1 1 2 1 2 0 0 1 1 2 1 1 1 1 0 0 2 0 1 1 2 0 1 0 0 2 1 2 1 0 2 0 2 2 2 1 1 2 0 1 1 1 2 2 0 2 1 2 2 2 0 1 0 1 0 1 0 1 2 0 2 2 0 2 0 0 0 1 2 1 2 0 0 1 0 0 1 2 2 2 0 2 1 0 2 0 0 2 0 2 2 1 1 2 0 2 2 2 0 1 1 1 2 1
0 2 0 2 2 1 2 1 1 0 1 1 1 0 0 0 2 1 1 2 0 2 0 1 0 2 0 1 0 0 0 0 0 2 0 1 2 1 0 2 1 1 1 2 0 2 2 1 2 0 0 0 0 0 2 1 1 1 2 1 2 0 2 2 1 2 0 2 2 0 1 1 2 2 0 1 1 0 1 0 2 0 1 2 2 0 1 0 2 1 2 0 0 2 0 1 0 0 2 0 2 0 1 0 1 2 0 1 0 1 1 0 2 1 0 2 1 2 0 0 2 0 2 1 0 2 0 1 2 0 1 0 2 1 0 1 0 1 1 1



Which is a code with the following weight distribution
1y17+1904x87y17+1176x90y17+2072x96y17+1008x99y17+344x105y17+56x108y17