In this paper, the use of coded transmit waveforms with post-beamforming nonlinear filtering of echo data in diagnostic ultrasound is presented. The nonlinear filter based on the second-order Volterra filter (SoVF) model separates the linear and quadratic echo components. The grayscale representation of the latter results in a new mode of imaging we refer to as quadratic B-mode (QB-mode). The use of chirp transmit waveforms in imaging contrast agents allows for nonlinear excitation of microbubble contrast agents (UCA) at a range of frequencies throughout the bandwidth of the transducer. The QB-mode image is shown to produce significant increase in UCA contrast over standard B-mode images from conventional and chirp excitation with and without compression. This contrast enhancement is achieved without loss in spatial resolution.