Data gathering operations in remote locations often rely on relay drones, which collect, store and deliver transmitted information to a ground control station. The probability of the ground control station successfully reconstructing the gathered data can be increased if random linear coding (RLC) is used, especially when feedback channels between the drones and the transmitter are not available. RLC decoding can be complemented by partial packet recovery (PPR), which utilizes sparse recovery principles to repair erroneously received data before RLC decoding takes place. We explain that the spark of the transpose of the parity-check matrix of the linear code, that is, the smallest number of linearly-dependent columns of the matrix, influences the effectiveness of PPR. We formulate a spark optimization problem and obtain code designs that achieve a gain over PPR-assisted RLC, in terms of the probability that the ground control station will decode the delivered data.