Microtubule self-organization is an important physical process underlying a number of essential cellular functions including cell division. In cell division, the dominant organization is the mitotic spindle, a football-shaped microtubule organization. We are interested in the underlying fundamental principles behind the self-organization of the spindle shape. Prior biological works have hypothesized that motor proteins are required for the proper formation of the spindle. Many of these motor proteins are also microtubule-crosslinkers, so it is unclear if the important aspect is the motor activity or the crosslinking. In this study, we seek to address this question by examining the self-organization of microtubules using crosslinkers alone. We use a minimal system composed of tubulin, an antiparallel microtubule-crosslinking protein, and a crowding agent to explore the phase space of organizations as a function of tubulin and crosslinker concentration. We find that the concentration of the antiparallel crosslinker, MAP65, has a significant effect on the organization and resulted in spindle-like organizations at relatively low concentration without the need for motor activity. Surprisingly, the length of the microtubules only moderately affects the equilibrium organization. We characterize both the shape and dynamics of these spindle-like organizations. We find that they are birefringent homogeneous tactoids. The microtubules have slow mobility, but the crosslinkers have fast mobility within the tactoids. These structures represent a first step in the recapitulation of self-organized spindles of microtubules that can be used as initial structures for further biophysical and active matter studies relevant to the biological process of cell division.