The authors consider a single-channel power line communication (PLC) system in the presence of Middleton Class-A impulsive noise employing multi-level amplitude-shift keying (ASK) modulation at the transmitter and non-coherent detection at the receiver. An asymptotically optimal detector for the PLC system is obtained using a tight approximation of the noise statistics. The magnitude of the received symbol is obtained as the decision variable, whose statistics is utilised to derive a series expression for the symbol error rate (SER). An asymptotic expression for the SER at high signal-to-noise ratio (SNR) is also obtained which is further utilised to find the optimal ASK constellation minimising the SER. It is shown by numerical examples that the optimal solution is extremely close to the equally spaced ASK constellation set at high SNR. It is also observed that the SER variation of the system with the impulsive index of the noise validates the optimality of the proposed detector at high SNR.