The generator matrix 1 0 0 1 1 1 X^2+X 1 1 1 1 X^2+X 0 X^2+X X^2+X X^2 1 0 1 1 1 1 1 X X 1 X 1 0 1 X^2+X 1 X 1 X^2 X 1 X^2 X^2 1 0 X^2+X 1 1 1 X^2+X 1 1 X^2 1 1 1 1 1 X^2+X X 1 1 X^2+X X^2+X 0 1 0 X^2 1 1 X 1 1 1 X 1 0 1 0 0 1 1 1 X X+1 X X+1 1 1 0 1 0 X^2 1 X^2 X+1 1 X^2+X+1 X^2 1 X^2 1 1 0 X^2 X^2+X 1 X+1 1 X 1 1 X^2+X+1 1 X 0 1 1 X^2 X^2+X+1 X^2+X+1 1 X^2+1 X+1 1 X^2+X X X^2+1 X X^2+X+1 X^2+X X^2+X 0 X 1 X^2+X 1 1 1 1 0 X 0 X+1 1 X 1 1 0 0 1 1 1 0 1 X^2+1 X^2 0 1 X+1 X^2 1 X^2+X 1 1 X^2+1 X^2+X 1 0 1 X^2+1 1 1 X^2+X 0 X^2+X 1 X^2 1 X^2+X X^2+X X^2+X+1 X^2+X+1 X^2 X^2+1 X+1 1 X+1 X^2+X X^2 X^2 1 X^2 X X^2 X^2+X 1 X X+1 X^2+1 1 X+1 1 1 0 X+1 X^2 1 X^2+X 1 X+1 X^2+X+1 X^2+X+1 X 1 X X X X^2+1 X^2+X 0 0 0 X 0 0 X^2 0 X^2+X X^2+X X X X X^2+X X X X^2+X X^2+X X^2+X X^2 X^2+X X 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2+X X^2 0 X^2 0 X^2 X^2+X X^2+X X 0 0 0 0 X X X^2 X X^2+X 0 X^2 X^2+X 0 X^2 0 0 X 0 X X X^2 X 0 X X 0 X^2+X X X^2 X^2 0 X^2+X 0 0 0 0 X 0 X X^2+X X X X^2 0 X X^2 X^2 X^2+X X^2+X X X^2 X^2 X^2 X 0 X^2 X^2+X X^2+X X X X X X^2 X^2+X X^2 0 X^2+X X^2+X 0 X X X^2+X X^2 0 X^2 X X^2 X 0 X X^2 X X X X^2+X 0 X^2 X^2+X X X^2 X^2 0 X X^2+X X^2+X X^2+X X^2 X X^2+X X X X^2+X 0 X^2 0 0 0 0 0 X X^2 X^2+X 0 X X^2+X X^2+X X^2+X X X^2+X X^2+X 0 X X X^2 X^2 X X^2+X 0 0 X 0 0 X X X^2+X X^2+X X^2+X X^2 X X^2+X X 0 0 X^2+X X X^2 X^2+X X^2+X X X^2+X 0 X^2 X^2 0 X^2+X X^2 0 X^2+X X^2 X^2 X^2 X^2+X 0 X^2 X^2+X X 0 0 0 X X X X^2 X^2 X^2+X X generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+234x^62+184x^63+907x^64+604x^65+1586x^66+1248x^67+2459x^68+1760x^69+3330x^70+2308x^71+3558x^72+2372x^73+3352x^74+1876x^75+2456x^76+1196x^77+1524x^78+500x^79+626x^80+208x^81+280x^82+28x^83+93x^84+4x^85+56x^86+12x^88+6x^90 The gray image is a linear code over GF(2) with n=288, k=15 and d=124. This code was found by Heurico 1.16 in 55.4 seconds.