Consider the problem of quantizing a Gaussian vector source. When the encoder can adapt to the correlation matrix of the source, the task is easily reduced to standard parallel quantization of scalar sources. We consider however quantization using a universal scheme, where the operation of the encoder is independent of the correlation matrix. This problem is analogous to coding over a open-loop (compound) multi-input multiple-output channel. Accordingly, we borrow techniques that were developed for the latter problem. In particular, we employ the recently introduced integer-forcing framework that works well for "most" correlation matrices. In order to provide performance guarantees for all correlation matrices, we apply a universal linear precoding operation based on space-time coding.