The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X 0 X 1 X 0 1 1 0 X 0 X X 1 1 0 X 1 1 1 1 X 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 0 0 0 X X 0 X X 0 X X X X 0 X 0 X 0 X 0 0 X X 0 X X 0 0 X X X X 0 X X X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 X 0 X 0 0 0 X X 0 X X 0 0 X X 0 0 X X 0 0 X 0 X 0 X 0 X 0 X 0 X 0 X 0 0 0 0 X X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 X X 0 X X 0 0 0 X X 0 X X 0 0 0 0 X X X 0 X 0 X 0 0 X X 0 0 0 0 X 0 0 X X X X 0 0 0 0 0 X X 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X 0 0 0 0 X X X X 0 0 0 X X X X X X X X X 0 0 X X 0 0 X X X X X 0 X X 0 0 0 X 0 X 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X 0 X X 0 0 0 0 0 0 0 X X X 0 X 0 0 X 0 0 X X X X 0 0 0 X 0 0 X X 0 0 X X X X 0 X X 0 X X X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 0 0 X X 0 0 X X X 0 0 0 X X 0 X 0 X 0 0 X X X 0 0 0 X X 0 0 0 X X X X 0 0 X X X 0 X X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X X X X 0 X 0 X X X X 0 X 0 0 0 X 0 0 X 0 X X X 0 0 X 0 0 0 0 0 X 0 0 0 0 X 0 0 X X X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 X 0 X X X 0 X X X 0 0 X X 0 X X X 0 0 X 0 0 X 0 X X X 0 0 0 X 0 0 X X X X 0 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X 0 0 X X 0 X X X X X 0 0 X 0 X 0 X 0 X X 0 0 X 0 0 X 0 0 0 X 0 X X 0 X 0 0 X X X X 0 X 0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 X 0 0 0 X 0 0 0 0 0 0 X X X X X 0 0 X 0 X 0 0 X X 0 0 X 0 0 0 0 0 X X X 0 0 X X 0 0 0 X 0 generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+66x^58+119x^60+185x^62+247x^64+304x^66+409x^68+469x^70+539x^72+494x^74+394x^76+305x^78+197x^80+140x^82+95x^84+59x^86+37x^88+20x^90+6x^92+6x^94+3x^96+1x^108 The gray image is a linear code over GF(2) with n=144, k=12 and d=58. This code was found by Heurico 1.16 in 92.6 seconds.