For 10 points, identify this first Japanese shogunate which ruled until 1333.
Following the death of this period's first leaders, Wada Yoshimori and members of his family were accused of treason and exiled. During this period, Yasutoki established a board of councilors called hyojoshu and appointed Kujō Yoritsune as leader. This period saw a revolt of sōhei forces stopped at the third battle of Uji, leading its instigator to be exiled to the Oki Islands. This government was led by a family that employed the Rokuhara Tandai, and it was faced with Go-Toba's abortive Jōkyū War. The tri-force enthusiasts Hōjō Clan also vied for power during this period. The defeat of the Taira clan in the Gempei War established this government, though Ashikaga Takauji established his own bakufu when this government ended. For 10 points, identify this first Japanese shogunate which ruled until 1333.
Following the death of this period's first leaders, Wada Yoshimori and members of his family were accused of treason and exiled.
Kamakura shogunate [accept "period" or "bakufu" in place of "shogunate"]