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While many communication systems experience extraneous noise that is well-modelled as Gaussian, experimental studies have shown that large values are more common when noise is impulsive and the Laplace distribution has been proposed as a more appropriate statistical model in that setting. Guessing Random Additive Noise Decoding is a class of forward error correction decoders that can avail of channel knowledge to improve decoding. Here we introduce a GRAND decoder that is specifically tailored to impulsive noise, which we call Laplace Ordered Reliability Bits GRAND (LORBGRAND). By adapting GRAND to the characteristics of Laplace noise we find an improvement of the order of ~1dB in block error rate, highlighting the benefits of noise-specific decoding strategies. Additionally, we extend the algorithm to provide soft output to indicate the probability estimation of correct decoding, which can be used to identify unreliable decoded signals.