The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 1 1 0 X 0 X 1 1 1 1 X^2+X 1 X^2+X X^2+X 1 1 1 X X^2+X X 1 1 1 1 0 1 X 1 1 1 0 X^2 0 1 X 1 1 1 1 1 X 1 1 1 X^2 1 X^2+X X 1 X^2+X X 1 1 1 1 0 X 1 1 1 1 1 X^2+X 1 1 1 X 1 1 1 1 1 1 1 1 0 1 0 0 1 X+1 1 X^2+X 0 X+1 X^2+X 1 1 1 X^2+X 1 1 X^2+1 X X^2+X 1 1 1 1 1 0 X^2 1 0 0 X X^2+1 X^2 X 1 1 X X+1 X^2+X X+1 1 X^2+X 1 X+1 1 X^2+X+1 X^2+X 1 0 X^2+1 1 X^2+X X^2+X+1 X^2+1 X X 1 1 X^2 1 1 X^2 X^2 X^2+1 1 0 X^2 X^2+1 0 0 X^2+X X 1 X^2+1 X^2+1 X^2+1 0 X^2+1 X X^2 X+1 X^2+X 0 X X^2+X 0 0 1 1 1 0 1 1 1 X^2+1 0 X^2 1 X^2 1 X^2+X X^2+X X+1 X^2+X X^2+X+1 1 X X^2+X X^2+X+1 X+1 0 1 0 1 1 1 X+1 X^2+X X^2+X+1 1 X 1 X^2 X^2 X^2+X+1 X^2 1 X^2+X+1 X X+1 X^2+X+1 X X 1 X^2+1 0 X^2+1 X X^2+1 1 0 X^2 X^2 0 X^2+X+1 X^2+X X+1 X^2+1 X 1 1 1 0 X^2+X+1 X+1 X^2+X+1 0 X^2+X X X^2+X 1 1 X^2+X+1 0 X 1 1 0 X^2+1 X^2+X 0 0 0 X 0 0 X^2 X^2 X^2 X^2+X X X X^2+X X X 0 X^2 X^2+X 0 X^2+X X X X 0 X^2 X^2+X X^2 X^2 X^2+X 0 X X^2+X 0 X^2 0 X^2+X X X^2 X 0 0 X X^2 0 0 X 0 X^2+X X 0 X^2 0 X X^2 X 0 X^2+X 0 X^2 X^2+X X^2 0 X^2+X X^2 X^2+X X^2+X X^2+X 0 X^2 X^2 X X^2+X X^2+X 0 X X^2 X X^2 X^2 X X^2+X X X 0 X^2 0 0 0 0 X X^2 X X^2+X X^2+X X^2 X X^2+X 0 X 0 X^2+X X X^2+X X X^2+X X^2+X X^2 0 0 0 0 0 X X X^2 X^2 X^2 0 X^2 X^2+X X 0 X X^2 X X X X^2 X^2 X X 0 0 X^2+X X^2 X^2 X^2+X 0 X^2 X^2+X X X^2+X 0 X X 0 X X 0 X^2 X^2+X X^2 X^2+X 0 X^2 0 X X^2 X^2+X 0 X^2+X X X^2 X^2 X^2 X 0 0 0 X^2+X generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+132x^77+314x^78+324x^79+664x^80+574x^81+714x^82+582x^83+816x^84+574x^85+659x^86+522x^87+525x^88+354x^89+453x^90+272x^91+217x^92+128x^93+144x^94+88x^95+64x^96+22x^97+17x^98+2x^99+15x^100+6x^101+2x^102+2x^103+2x^104+2x^105+1x^110 The gray image is a linear code over GF(2) with n=340, k=13 and d=154. This code was found by Heurico 1.16 in 4.56 seconds.