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.).
Sources:
- Tortoises in Space - 46BLYZ
- Zond 7 - NASA
- Lunar Perigee and Apogee Calculator - John Walker
- Experiments with micro-organisms and human cell cultures in the Zond 5 and Zond 7 flights - Zhukov-Verezhnikov NN, Volkov MN, Maisky IN, Rybakov NI, Guberniev MA, Podoplelov II, Kulagin AN, Aniskin ED, Rybakova KD, Sharyi NI, Voronkova IP, Saxonov PP, Kopyev VY, Antipov VV, Kozlov VA, Parfyonov GP, Orlovsky VI