A combination of phenomenological analysis and Mössbauer spectroscopy experiments on the tetragonal Fe(1+y)Te 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 Mössbauer spectra at temperatures above the antiferromagnetic transition. The incommensurate spin-density wave order in Fe(1+y)Te 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.