The generator matrix 1 0 0 1 1 1 X^2+X 1 X 1 X 1 1 X^2 1 X^2+X X^2+X 1 1 X^2+X 1 0 X^2 0 1 1 1 1 1 1 1 X^2+X X^2+X X 1 1 X 1 1 1 0 1 X 1 1 X^2+X 1 X^2 1 1 X 1 X^2 X^2+X 1 X^2 0 1 1 1 0 1 0 X^2 1 1 X^2+X X^2 0 1 X X^2 1 1 X^2+X 1 1 0 X X X^2 1 0 1 1 X^2+X 1 1 1 0 X^2 0 1 0 0 1 X+1 1 X^2 X^2 0 1 X^2+X+1 1 1 0 1 1 0 1 X^2 1 X^2+X 1 1 1 X^2+X X+1 X X^2+1 1 X X 1 1 X^2+X X^2+X+1 1 1 X^2+X X^2+X 1 X^2+1 0 X^2+1 X^2 1 X^2+1 1 X^2+X 0 X X X X^2 X+1 1 X X^2+1 X^2+1 X^2 0 X^2+X+1 1 1 1 X^2+X+1 X^2+X 1 1 X^2+1 1 1 X^2 0 1 X+1 X^2+X 1 1 1 1 X^2+1 X X X+1 1 X X^2+X X^2+X 1 0 0 0 1 1 1 0 1 X^2+1 1 X^2 0 X^2+X+1 0 X^2+1 X+1 X^2+1 X^2 X^2 0 1 1 1 0 X^2+1 X^2+X X^2 X^2+X+1 X+1 X+1 X^2 X^2+1 1 X^2+X X^2+X+1 X^2+X X^2+X X^2+X+1 X^2+X+1 X^2+1 X^2+X 0 X 1 X X^2+1 X X+1 X^2 X^2+X+1 0 1 1 1 1 X^2+1 X^2+X+1 1 X^2+X X+1 X^2+X+1 1 X^2+1 0 X+1 X^2 0 1 X^2+1 1 X X^2+X+1 1 1 X^2+X 0 X+1 X X^2+X+1 0 X^2 X^2+1 X^2+X+1 1 X^2+X X^2+X X^2+X 0 1 X^2+1 0 1 0 0 0 X 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2+X X X^2+X X X X^2+X X^2+X X X X X X^2+X X 0 0 0 0 X X^2 0 X X X^2 X X^2+X 0 X X X^2+X X^2 X^2 0 X 0 X^2+X X^2+X X^2+X X 0 X^2+X X 0 X^2 X^2+X X X^2 0 X^2+X X^2 X^2 X^2+X X^2 X^2 X 0 0 0 X 0 X^2+X X^2 X X^2 X^2 X^2+X 0 X^2+X 0 X X^2+X X X^2+X 0 X^2 X X 0 0 0 0 X X^2 X X X^2+X X X X^2 X^2+X X^2 X^2 0 X^2 0 0 X^2 X^2+X X^2+X X X^2+X X^2+X X 0 X^2+X 0 0 X^2+X X^2 X X^2 X^2 X X^2 X^2+X X^2+X X^2 X X^2 X^2+X 0 0 0 X 0 X^2+X X^2+X 0 X^2 X^2 0 X^2+X X^2+X 0 X X X^2+X X^2 X X^2 X^2+X 0 X X^2+X X 0 0 X^2 X^2+X X^2 0 X^2+X 0 X^2+X X X^2+X X X^2 X^2+X X^2+X X X X^2 X^2+X 0 0 X^2 X^2 generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 83. Homogenous weight enumerator: w(x)=1x^0+162x^83+378x^84+414x^85+508x^86+634x^87+640x^88+674x^89+653x^90+620x^91+594x^92+542x^93+502x^94+450x^95+403x^96+268x^97+210x^98+164x^99+98x^100+108x^101+60x^102+46x^103+24x^104+6x^105+17x^106+2x^107+2x^108+4x^109+2x^110+2x^111+4x^112 The gray image is a linear code over GF(2) with n=364, k=13 and d=166. This code was found by Heurico 1.16 in 12.7 seconds.