Shape memory polymers (SMPs) are stimuli-responsive materials, which are able to retain an imposed, temporary shape and recover the initial, permanent shape through an external stimulus like heat. In this work, a novel manufacturing method is introduced for thermoresponsive quick response (QR) code carriers, which originally were developed as anticounterfeiting technology. Motivated by the fact that earlier manufacturing processes were sometimes too time-consuming for production, filaments of a polyester urethane (PEU) with and without dye were extruded and processed into QR code carriers using fused filament fabrication (FFF). Once programmed, the distinct shape memory properties enabled a heating-initiated switching from non-decodable to machine-readable QR codes. The results demonstrate that FFF constitutes a promising additive manufacturing technology to create complex, filigree structures with adjustable horizontal and vertical print resolution and, thus, an excellent basis to realize further technically demanding application concepts for shape memory polymers.