Imaging genetic studies of large control cohorts such as UK Biobank enable to assess the range of normal variations in brain structures. Previous studies by our group have shown that the width of several cortical sulci is associated with a variant in the upstream region of KCNK2 gene even if this effect is corrected with age. Here we propose to analyze in a multivariate setup the associations between sets of genetic variants and multiple sulci widths. The genetic variants we consider are sets of SNPs of known phase called haplotypes, taken from the upstream region of KCNK2 gene. To the best of our knowledge, multivariate analysis in imaging genetics has never been used in haplotype studies. Our method was able to recover the expected association signal and uncover new associations between imaging data and genetic variants.