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 X^2 X X X X^2 1 0 0 1 X^2 X 0 X 1 1 X 1 0 X^2 1 1 0 1 0 X^2 0 1 1 X 1 X^2 1 1 1 1 1 1 1 1 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 X^2 X^2+X X^2 X X X^2 X X X X^2 X X 0 X^2 X^2 X^2 X^2 X X^2 X^2 X X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2 X X X 0 0 X X^2 X X^2 0 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X^2 X X 0 X X^2 X 0 0 X^2+X X^2+X X X^2 0 X^2 X X^2 X^2 X X^2 0 0 X 0 X X X^2 X^2+X X 0 X^2 X^2 X^2+X 0 X^2+X X^2+X X^2 X 0 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X X^2 X X^2+X 0 0 0 X X X^2 X X^2 X X^2+X X^2 X^2+X X^2+X 0 X X^2+X 0 X^2 X^2+X X^2 X 0 X^2 X^2 X^2+X X^2 X^2 X 0 X^2 0 X^2 X 0 X 0 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X 0 0 X^2 0 X 0 X X^2 0 X^2 X X^2+X 0 0 X^2+X X X^2+X 0 X^2 X X^2 X^2 0 X^2+X X^2+X X^2 X^2 0 X^2 X X^2 X^2 X^2+X 0 X^2 X^2 X 0 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 X X 0 X^2+X X^2 X^2 X^2 X^2+X X^2+X X X^2+X X X^2+X 0 0 0 X^2+X X^2 0 X X 0 X^2+X X^2 0 X^2 X^2 X^2 X X X^2 0 X^2+X 0 X^2 X^2+X X^2 0 X^2 generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+34x^66+90x^67+164x^68+198x^69+261x^70+332x^71+393x^72+386x^73+530x^74+708x^75+702x^76+784x^77+728x^78+598x^79+487x^80+472x^81+352x^82+226x^83+220x^84+150x^85+91x^86+68x^87+67x^88+46x^89+42x^90+24x^91+10x^92+12x^93+8x^94+2x^95+4x^96+1x^98+1x^114 The gray image is a linear code over GF(2) with n=308, k=13 and d=132. This code was found by Heurico 1.16 in 6.91 seconds.