Advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Greenlaw et al. (Bioinformatics, 2017) have recently developed a Bayesian group sparse multi-task regression model for imaging genetics based on a three-level Gaussian scale mixture formulation. The model makes certain simplifying assumptions on the covariance structure of the imaging phenotypes, and in this work we extend the model to allow for more generality. Specifically, our new model accommodates two forms of response correlation: (i) spatial correlation between imaging phenotypes on the same hemisphere of the brain, and (ii) bilateral correlation between related phenotypes on opposite hemispheres of the brain. A Bayesian group lasso prior is adopted for the regression parameters corresponding to each SNP across all regions of interest. We present and compare a fully Bayesian and a variational Bayes implementation of the model along with a comparison to the original non-spatial model in simulation studies and an application to data obtained from the Alzheimer's Disease Neuroimaging Initiative.