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 X 1 X 1 X X 1 1 1 1 X 1 1 X 1 1 X^2 1 1 0 X 1 X 1 1 1 X^2 X^2 X X 1 1 X X^2 0 X 0 0 0 X X^2+X X 0 X^2 X^2 0 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 0 0 X^2+X X^2 X^2+X 0 X^2 X X X^2 X X 0 X^2+X X^2 0 X X^2+X 0 X^2+X X^2 X^2+X X 0 X^2+X X^2+X X^2 X^2 X 0 X^2 X^2 0 0 X^2+X X^2+X 0 X^2+X X 0 X^2+X X^2+X X^2 X^2 X X 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 0 X X^2 0 X^2+X X^2+X X^2 X^2+X X^2 0 X^2 X X^2 X X X X^2 0 0 X X^2 X X^2 X^2+X X^2+X X^2+X X X^2 0 X X X^2 0 X^2+X 0 0 0 X X^2+X X^2 X X 0 X^2+X 0 X^2+X 0 X^2 X^2 X X^2 0 0 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2 X X X^2 0 X^2+X 0 X X^2 X X 0 0 X X^2 X^2+X X^2+X X X X^2+X X^2+X X^2+X 0 X^2 0 0 X^2 X^2 X 0 X X^2+X X^2 X^2+X X X^2+X X 0 X X X^2 X X^2 X^2 X^2+X X^2 0 X X^2 X X^2 X X X 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+184x^58+16x^59+311x^60+72x^61+384x^62+136x^63+494x^64+256x^65+485x^66+320x^67+416x^68+168x^69+328x^70+40x^71+209x^72+16x^73+129x^74+84x^76+19x^78+20x^80+6x^82+1x^86+1x^100 The gray image is a linear code over GF(2) with n=264, k=12 and d=116. This code was found by Heurico 1.16 in 1.66 seconds.