The reaction 4He(π-π+) at an incident π- energy of 165 Mev has been measured at 0° in a search for bound states of the tetraneutron and resonant states in the continuum. No resonant structure was observed, and a cross section of 7 ± 15 nb/sr has been determined for bound tetraneutron production by this reaction. The measured cross section magnitudes are consistent with the related measurements of Falomkin et al and Stetz et al, but are larger than the results of Kaufman et al and the calculations of Gibbs et al by a factor of at least 100. The relevance of these results to identification of the pion double charge exchange reaction mechanism is discussed.