We study the performance of locally decodable sparse quantum codes. The most familiar example of such a code is Kitaev’s toric code. During the last ten years, a number of different constructions of these codes appeared, for example: surfaces codes, finite geometry codes or Latin square codes. These codes are defined by stabilizer group with generators of low weight. If the stabilizer matrix has row weight m and column weight l, we talk about a (l,m) code. Our main result is an upper bound on achievable rates of stabilizer (l,m) codes, as a function of m and l. Achievable rates are rates for which decoding is possible with high probability.