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 0 1 1 1 1 1 1 X^2 1 1 1 1 X^2 1 1 1 1 1 1 0 1 X^2 1 X 1 1 0 1 0 1 1 1 X 0 1 X^2 0 1 X X X 1 1 X 1 0 X 0 0 0 X X^2+X X X^2 X^2 X 0 0 X X X^2+X 0 0 X^2+X X X^2 X X^2+X X^2 X^2 0 X^2 X X^2+X X 0 X^2+X X X^2+X X^2 0 X X^2 X^2+X X^2 0 X^2 X^2+X X^2+X 0 0 X^2+X X 0 X X X^2 0 X^2 0 X^2 X X^2+X 0 X^2+X X^2 X X X X 0 0 0 X^2 X X^2 0 X^2+X X^2 X X^2+X X^2 X^2 X X^2 X 0 X X X X^2 0 0 X 0 X X X 0 X^2 0 X^2+X X X^2+X 0 X^2+X 0 X^2 X^2+X X^2 X^2+X 0 X^2 X X 0 0 X X X^2 X^2+X X X^2 0 0 X 0 X^2 X X X^2+X X^2 X X^2+X X^2 0 0 X^2+X 0 X X^2+X X 0 X^2 X X 0 X^2 X X^2+X X X^2 X^2 X 0 X 0 0 X X^2+X X^2+X X^2 X^2 0 X^2+X X^2 0 X X X X X^2+X X^2 0 0 X X 0 0 0 X X 0 X X^2+X 0 X X^2 X X^2 X^2+X X 0 X^2 X X 0 X^2+X X^2 X^2+X X^2 X^2+X 0 X X^2+X 0 0 X^2 X X^2+X X^2+X 0 0 0 X^2+X X X^2+X X 0 X 0 X X^2 X^2 0 X X^2 X^2+X X^2 X X X^2+X X X^2 0 X X^2 X 0 X^2 X 0 X^2+X X^2 X^2 X 0 X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X X^2+X 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 0 X^2 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 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+67x^78+183x^80+24x^81+229x^82+92x^83+238x^84+148x^85+217x^86+136x^87+211x^88+80x^89+168x^90+28x^91+78x^92+4x^93+57x^94+39x^96+23x^98+11x^100+7x^102+6x^104+1x^140 The gray image is a linear code over GF(2) with n=344, k=11 and d=156. This code was found by Heurico 1.16 in 0.862 seconds.