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3 down vote accepted The animals sent farthest from the Earth were the tortoises (and other creatures, see below) on Zond 7. They were sent roughly 407,000 km from the center of the Earth (possibly more depending on whether the distance of Zond 7 from the moon was calculated from the surface or the center).
Regarding what was on board, there is an overview paper "Results of Biological Investigations Undertaken on the Zond-5, Zond-6 and Zond-7 Stations" Gazenko, O. G.; Antipov, V. V.; Parfenov, G. P. Cosmic Research, Vol. 9, p.548 which is a translation from Russian "Kosmicheskie Issledovania" journal.
It states that Zond 5 and 7 were identical by animal selection. It included: Turtles, Drosophila, Tradescantia, Allium cepa (onion), dry seeds of Rye, different strains of Chlorella, and E. coli and other biological objects.
Human tissue samples were also on board according to another paper (Zhukov-Verezhnikov, et al.).