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In this paper, we prove a stability result on k mod p multisets of points inPG(2,q), q = p^h. The particular case k=0 is used to describe small weightcodewords of the code generated by the lines of PG(2, q), as linear combinationof few lines. Earlier results proved this for codewords with weight less than2.5q, while our result is valid until cq sqrt(q). It is sharp when 27<q squareand h>=4. When q is a prime, De Boeck and Vandendriessche constructed acodeword of weight 3p-3 that is not the linear combination of three lines. Wecharacterise their example.

Stability of k mod p multisets and small weight codewords of the code generated by the lines of PG(2, q)