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Codes defined through the row-span over finite fields of incidence matrices of designs have many properties that can be deduced from the combinatorial properties of the designs. In particular those codes that come from designs defined by finite geometries have been used both in applications and for classification purposes within design theory. We look here at their applicability to a method of decoding that was introduced by MacWilliams in the early 60s, viz. permutation decoding. Her notion of PD-sets is generalized to that of partial PD-sets that can be used to correct some number of errors possibly less than the full capability of the code. These have been found for some infinite classes of codes from finite planes and graphs