Ibukiyama's student Tomoya Kiyuna proved $Sym^8$ for $Sp(n,\mathbb{Z})$ in his Master's thesis. Here I haven't got any link or reference.

AFAIK he uses similar techniques as Ibukiyama for $Sym^4$ and $Sym^6$.

ncr commented on the proof [in this mathoverflow thread][1] :

>I wrote to Kiyuna and he tells me that there are 18 generators: 6 of them are theta series (presumably products of theta constants) and the remaining 12 are a kind of Rankin-Cohen construction. I don't know much more but he tells me there will be a preprint in the next couple of weeks. 


  [1]: http://mathoverflow.net/questions/102575/are-there-cusp-forms-for-the-full-modular-group-sp2-z-and-representations-det