The generator matrix 1 0 0 0 1 1 1 X^2 X 1 1 0 X^2 1 1 1 X^2+X X^2+X X^2 1 1 1 X^2+X 0 0 1 X^2 1 1 1 X^2 1 X X^2+X 1 X^2+X X^2 X^2+X X 1 1 1 1 X^2 1 X X^2+X 1 1 1 X^2 1 1 X^2+X 1 X^2+X X 1 1 X 1 X^2 1 X 1 X X^2 X X^2 X^2+X 0 X^2+X 1 1 1 X 1 0 X^2 0 1 1 1 1 1 1 0 1 0 0 1 X^2 1 0 1 1 X^2 1 1 X 1 X^2+X 1 1 X X+1 X^2+X X^2+X X X^2+X 1 1 1 0 1 X^2+X+1 1 X^2+X X^2+X 1 X 1 1 0 0 X X X^2+1 1 1 X+1 0 1 1 X 0 1 0 X 1 X^2 1 1 0 X+1 X^2 X X^2+X X X^2+X X^2+X 1 X^2+X X 1 1 X X^2+X X^2+1 X^2+X X+1 1 X+1 X^2 1 1 X^2 0 X^2 1 X^2+X 0 0 0 1 0 X 0 X^2+X 1 X^2 X^2+X+1 1 X^2+X+1 X^2+X+1 1 X^2+1 X+1 1 X^2 1 0 X^2+X 0 1 X^2 X X^2 1 X^2+1 1 X^2+X+1 X^2+1 X^2+X 1 X^2+X X^2+1 X+1 X^2 X 1 0 X^2+1 1 X^2+X+1 0 X 0 X^2+X+1 X^2+X X^2 X+1 X X^2+X X^2+X+1 X^2+X+1 X X+1 X X^2+X+1 X 1 X 0 1 1 X+1 X^2+X+1 1 1 X^2+1 X^2+X 1 1 X+1 X^2+X X+1 X^2+1 0 0 X+1 X+1 X^2 1 0 X^2+X X 0 0 0 0 1 X 1 X+1 1 1 X^2+1 X^2+X X^2+X X+1 X+1 X^2 0 X^2+1 X^2+X+1 0 X^2+X X^2+X X+1 X^2+X+1 1 0 X^2+X+1 X^2+X X+1 X^2+X+1 X X+1 X+1 0 X^2 X^2+1 X^2+X 1 1 X+1 0 X^2 X^2+1 X^2 0 1 1 0 1 0 X^2+X+1 X^2+1 1 X^2+X X^2+1 0 X^2+X X^2+X X+1 1 1 X+1 1 X X^2+X+1 X^2+1 X+1 X^2+X X^2 X^2+1 X^2 X 1 X X^2+X X^2 X^2+X 0 1 X X^2+1 X+1 X^2 X+1 X^2+1 X^2 1 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 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+86x^78+340x^79+412x^80+568x^81+709x^82+642x^83+718x^84+640x^85+602x^86+584x^87+540x^88+434x^89+408x^90+470x^91+295x^92+224x^93+179x^94+106x^95+109x^96+66x^97+17x^98+16x^99+5x^100+4x^101+15x^102+2x^103 The gray image is a linear code over GF(2) with n=344, k=13 and d=156. This code was found by Heurico 1.11 in 1.61 seconds.