Determining rational points on modular curves is an important problem in arithmetic geometry; those curves which have Jacobian rank at least equal to the genus remain the frontier. While quadratic Chabauty can be an effective p-adic tool for computing rational points on certain modular curves where the rank of the Jacobian equals the genus, many of the underlying computations, such as computing a basis of de Rham cohomology, as well as the local height computations, become computationally prohibitive for higher genus non-split Cartan modular curves.  We will discuss joint work in progress with Steffen Mueller and Jan Vonk to carry out quadratic Chabauty on the genus 8 non split Cartan modular curve $X_{ns}^+(19)$  and what remains to be done to complete the quadratic Chabauty computation.