Enhanced index tracking (EIT) aims to achieve better performance over a target equity index while maintaining a relatively low tracking error. It can be formulated as a quadratic programming problem, but remains challenging when several practical constraints exist, especially the fixed number of assets in the portfolio. In this paper, we propose a new method for enhanced index tracking, subject to common practical constraints, including cardinality. Our method is based on a novel reparametrisation of portfolio weights, integrated with a stochastic optimisation for ranking the assets. It can simultaneously tackle asset selection and capital allocation, while being optimised by vanilla gradient descent effectively and efficiently. The proposed method is backtested with S&P 500 and Russell 1000 indices data for over a decade. Empirical results demonstrate its superiority over widely used alternatives.