Producción CientíficaIn this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field F4Ministerio de Economía, Industria y Competitividad (MTM2013-45588-C3-1-P / MTM2015-65764-C3-1-P / MTM2015-69138-REDT)Principado de Asturias (GRUPIN14-142