A combination of phenomenological analysis and Mossbauer spectroscopy experiments on the tetragonal Fe1+yTe system indicates that the magnetic ordering transition in compounds with higher Fe excess, y >= 0.11, is unconventional. Experimentally, a liquidlike magnetic precursor with quasistatic spin order is found from significantly broadened Mossbauer spectra at temperatures above the antiferromagnetic transition. The incommensurate spin-density wave order in Fe1+yTe is described by a magnetic free energy that violates the weak Lifshitz condition in the Landau theory of second-order transitions. The presence of multiple Lifshitz invariants provides the mechanism to create multidimensional, twisted, and modulated solitonic phases.