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We introduce a modification of the PyUltraLight code that models the dynamical evolution of ultralight axionlike scalar dark matter fields. Our modified code, PySiUltraLight, adds a quartic, self-interaction term to reflect the one which arises naturally in axionlike particle models. Using a particle mass of $10^{-22}~\mathrm{eV}/\mathrm{c}^2$, we show that PySiUltraLight produces spatially oscillating solitons, exploding solitons, and collapsing solitons which prior analytic work shows will occur with attractive self-interactions. Using our code we calculate the oscillation frequency as a function of soliton mass and equilibrium radius in the presence of attractive self-interactions. We show that when the soliton mass is below the critical mass ($M_c = \frac{\sqrt{3}}{2}M_{\mathrm{max}}$) described by Chavanis [arxiv:1604.05904] and the initial radius is within a specific range, solitons are unstable and explode. We test the maximum mass criteria described by Chavanis [arxiv:1604.05904] and Chavanis and Delfini [arxiv:1103.2054] for a soliton to collapse when attractive self-interactions are included. We also analyze both binary soliton collisions and a soliton rotating around a central mass with attractive and repulsive self-interactions. We find that when attractive self-interactions are included, the density profiles get distorted after a binary collision. We also find that a soliton is less susceptible to tidal stripping when attractive self-interactions are included. We find that the opposite is true for repulsive self-interactions in that solitons would be more easily tidally stripped. Including self-interactions might therefore influence the survival timescales of infalling solitons.