(This should be 1 + 35, the number of D.O.F 's of a ~self-dual~ rank 4 antysymmetric tensor in 8 dimensions:)
Length[SymmetrizedArrayRules[sa4sum]]
71
The right number 35 is of course hidden in this, because one cannot just count the length of SymmetrizedArrayRules[sa4sum]: there are now linear dependencies between them: let's define the sa4 a bit more convenient
In[71]:= Clear[sa4, sa4sum, sa4star]
sa4 = SymmetrizedArray[pos_ :> a @@ pos, {8, 8, 8, 8}, Antisymmetric[All]];
do the self-dualization
In[73]:= sa4star = HodgeDual[sa4];
In[74]:= sa4sum = sa4 + sa4star;
In[75]:= sa4sum == HodgeDual[sa4sum]
Out[8]= True
and now count correctly
In[56]:= Remove[coRank]
coRank[a_Plus, b_Plus] := MatrixRank[{List @@ a, List @@ b}]
In[76]:= Length[Partition[SortBy[Most[Last /@ SymmetrizedArrayRules[sa4sum]], coRank], 2]]
Out[76]= 35
the SortBy[] with coRank[] pairs linear dependent coefficients and there are 35 such pairs. Control it the other way around
In[79]:= coRank @@@ Partition[SortBy[Most[Last /@ SymmetrizedArrayRules[sa4sum]], coRank], 2]
Out[79]= {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}