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We characterise the minimum weight codewords of the p-ary linear code of intersecting lines in PG(3,q), q = p^h, q ≥ 19, p prime, h ≥ 1. If q is even, the minimum weight equals q³ + q² + q + 1. If q is odd, the minimum weight equals q³ + 2q² + q + 1. For q even, we also characterise the codewords of ...