Soliton turbulence is studied within the framework of Gardner equation (generalized Korteweg–de Vries equation including quadratic and cubic nonlinear terms) by virtue of the direct numerical simulation of the ensemble dynamics. This equation allows the different soliton polarities to exist which make possible waves with extreme amplitudes to occur. Though the pairwise soliton collisions happen more frequently in the soliton gas, multiple soliton collisions have been identified as well involving up to five solitons. The emergence of abnormally large waves (rogue waves) of “unexpected” polarity is demonstrated. Different statistical properties of soliton turbulence (statistical moments, distribution functions) are analyzed. •Dynamics of soliton ensembles is studied numerically within the Gardner equation.•Abnormally large wave emergences of “unexpected” polarity are demonstrated.•Multiple soliton collisions occur in a soliton gas.•The tail of the negative wave amplitude distribution function extends with time.