The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X X 1 X 1 0 1 1 X 1 X 0 1 X X 1 1 1 0 X 1 1 1 1 1 0 1 0 1 1 1 1 0 X 0 1 1 1 1 0 0 X 1 1 0 0 X 0 1 1 1 0 1 0 0 0 1 1 1 0 X X+1 X+1 1 1 0 X 0 X+1 1 0 1 0 X+1 1 1 0 X X X 0 X+1 1 X X+1 0 X+1 0 1 1 0 1 0 X+1 1 X+1 0 1 X X+1 1 X+1 1 1 0 X 1 1 0 0 1 X X+1 X+1 0 0 0 1 0 1 1 0 1 0 1 1 X 0 1 1 0 1 1 X+1 X+1 1 1 X X+1 0 X 0 1 X+1 1 X 0 1 X X X+1 X+1 X 1 1 X X+1 X+1 1 1 1 X+1 X 0 0 X 0 X+1 1 1 X+1 X+1 1 1 X 0 0 X+1 0 0 0 0 1 1 0 1 1 1 0 X+1 X 1 X 1 1 X 1 X+1 0 0 0 1 0 1 X 1 1 X 1 0 X 1 X+1 X+1 1 0 X+1 X X+1 X+1 1 0 X 1 X+1 X 1 1 0 X+1 X+1 1 1 0 X+1 X X 1 X 1 X+1 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X X 0 X X X 0 0 X X X X X X X 0 0 0 X X 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X 0 X X X X X X X X X 0 0 0 0 0 0 0 X X 0 0 X 0 X 0 X X 0 X X 0 0 X 0 X X 0 X X 0 X 0 0 X X X X X X 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 0 0 0 0 X 0 X X X X X 0 X 0 X X 0 X X 0 X X 0 0 X 0 X X 0 0 0 0 X X 0 X 0 0 0 X X 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 0 0 X 0 X X X 0 0 X X X X X X 0 0 X 0 0 0 0 X 0 X 0 0 0 X 0 0 X X 0 0 0 X X 0 0 X 0 X X 0 X 0 X X 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 X 0 0 0 0 0 X X 0 0 0 X 0 0 X 0 0 0 X X 0 0 X 0 X X 0 0 X 0 0 0 0 X X 0 X X 0 X 0 0 X X 0 generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+47x^52+96x^53+172x^54+228x^55+278x^56+316x^57+352x^58+426x^59+480x^60+446x^61+453x^62+512x^63+529x^64+554x^65+558x^66+480x^67+402x^68+448x^69+359x^70+304x^71+230x^72+164x^73+117x^74+86x^75+65x^76+18x^77+31x^78+12x^79+10x^80+6x^81+4x^82+5x^84+1x^86+1x^90+1x^92 The gray image is a linear code over GF(2) with n=128, k=13 and d=52. This code was found by Heurico 1.16 in 9.68 seconds.