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 X X 1 1 X^2 X 0 0 1 X X^2 X^2 1 X X^2 0 1 X^2 X 1 1 1 X 1 X X 1 X^2 0 1 X X 1 X X^2 1 1 X 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2+X 0 0 X^2+X X X^2 0 0 X 0 X^2 X^2 X X X^2 X^2 0 X X X X^2 X^2 0 0 X^2 X 0 X X X^2+X 0 X^2 X^2 0 X 0 0 X X^2 X^2 X^2 X X^2+X X^2+X X X X X^2+X X X^2 X X X X^2+X X^2+X 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2+X X^2 X^2 X X X^2 X X^2+X 0 X^2+X 0 X^2+X X^2+X 0 0 X X X X^2 X^2+X X X^2+X X 0 X^2 X^2 X^2+X X 0 X^2 X X^2+X X X X^2 X^2+X X^2+X 0 0 0 0 X^2+X 0 X X X^2+X 0 X^2+X X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X^2+X X 0 X 0 X X 0 X^2 0 X X X^2+X X^2+X X^2+X X^2+X X^2 X 0 0 X^2 X X^2+X X X X^2+X X X^2+X X^2+X X^2+X 0 X X^2+X X X X^2 X^2 X^2 0 X X^2+X X X^2+X 0 X^2+X X^2 X^2+X X X^2 0 X X^2+X X^2+X 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+162x^66+4x^67+401x^68+60x^69+635x^70+240x^71+772x^72+748x^73+793x^74+1288x^75+906x^76+1768x^77+984x^78+1728x^79+876x^80+1288x^81+817x^82+788x^83+710x^84+220x^85+495x^86+48x^87+340x^88+12x^89+167x^90+67x^92+38x^94+19x^96+5x^98+3x^100+1x^108 The gray image is a linear code over GF(2) with n=312, k=14 and d=132. This code was found by Heurico 1.16 in 30.2 seconds.