Huntington's disease (HD) is a neurodegenerative disorder caused by an expansion mutation of the cytosine-adenine-guanine (CAG) trinucleotide in the HTT gene. Decline in cognitive and motor functioning during the prodromal phase has been reported, and understanding genetic influences on prodromal disease progression beyond CAG will benefit intervention therapies. From a prodromal HD cohort (N=715), we extracted gray matter (GM) components through independent component analysis and tested them for associations with cognitive and motor functioning that cannot be accounted for by CAG-induced disease burden (cumulative effects of CAG expansion and age). Furthermore, we examined genetic associations (at the genomic, HD pathway, and candidate region levels) with the GM components that were related to functional decline. After accounting for disease burden, GM in a component containing cuneus, lingual, and middle occipital regions was positively associated with attention and working memory performance, and the effect size was about a tenth of that of disease burden. Prodromal participants with at least one dystonia sign also had significantly lower GM volume in a bilateral inferior parietal component than participants without dystonia, after controlling for the disease burden. Two single-nucleotide polymorphisms (SNPs: rs71358386 in NCOR1 and rs71358386 in ADORA2B) in the HD pathway were significantly associated with GM volume in the cuneus component, with minor alleles being linked to reduced GM volume. Additionally, homozygous minor allele carriers of SNPs in a candidate region of ch15q13.3 had significantly higher GM volume in the inferior parietal component, and one minor allele copy was associated with a total motor score decrease of 0.14U. Our findings depict an early genetical GM reduction in prodromal HD that occurs irrespective of disease burden and affects regions important for cognitive and motor functioning.