From Wikipedia:
Longevity
Basenjis in the 2004 UK Kennel Club survey had a median lifespan of 13.6 years (sample size of 46 deceased dogs),[6] which is 1–2 years longer than the median lifespan of other breeds of similar size.[7] The oldest dog in the survey was 17.5 years. Most common causes of death were old age (30%), urologic (incontinence, Fanconi syndrome, chronic kidney failure 13%), behavior ("unspecified" and aggression 9%), and cancer. (9%).[6]
Among 78 live dogs in the 2004 UKC survey, the most common health issues noted by owners were dermatologic and urologic[6] (urologic issues in Basenjis can be signs of Fanconi syndrome).<<
That was for a specific study, but if your grandmother has vet records, it would be fantastic for her to send them into her basenji club! I have heard of a few 17 and 18 yr olds, so am sure older are out there like your grandmother's.