Dawson's Chess Grundy Value

Dawson's chess is the octal game .137, whose Grundy values g(n) for n = 0,1,2,... are the well-known sequence 0,0,1,1,2,0,3,1,1,0,3,3,2,2,4,0,5,... (eventually periodic with period 34). In this game a position made of several independent strips is a win for the mover iff the XOR of the strips' Grundy values is nonzero. Using the published sequence, what is g(8)?