They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
The Tigers are looking to sweep the 2-match series after posting a comprehensive 48-run win in the first game.
They have made three changes to the line-up for Wednesday with seamer Hasan Mahmud winning his first cap.
Teams
Bangladesh XI: Mohammad Naim, Liton Das, Soumya Sarkar, Mushfiqur Rahim (wk), Mahmudullah (capt), Mahedi Hasan, Afif Hossain, Mohammad Saifuddin, Mustafizur Rahman, Al-Amin Hossain, Hasan Mahmud
Zimbabwe XI: Tinashe Kamunhukanmwe, Bredan Taylor, Craig Ervine, Wesley Madhevere, Sean Williams (capt), Sikandar Raza, Richmond Mutumbami (wk), Tinotenda Mutombodzi, Carl Mumba, Chris Mpofu, Charlton Tshuma