Access to medical data is highly regulated due to its sensitive nature, which can constrain communities' ability to utilize these data for research or clinical purposes. Common de-identification techniques to enable the sharing of data may not provide adequate privacy in every circumstance. We investigate the ability of Generative Adversarial Networks (GANs) to generate synthetic, and more significantly, multichannel electrocardiogram signals that are representative of waveforms observed in patients to address these privacy concerns. Successful generation of high-quality synthetic time series data has the potential to act as an effective substitute for actual patient data. For the first time, we demonstrate a range of novel loss functions using our multivariate GAN architecture and analyse their effect on data quality and privacy. We also present the application of multivariate dynamic time warping as a means of evaluating generated time series. Quantitative evidence demonstrates that the inclusion of a penalisation coefficient (Dynamic Time Warping) in the loss function enables our GAN to outperform the other generative models and loss functions explored by 4.9% according to our metrics. This allows for the generation of data that is more representative of the training set and diverse across generated samples, all whilst ensuring sufficient privacy.