The generator matrix 1 0 0 0 1 1 1 X^2 1 1 0 1 1 0 X 1 X^2+X 1 1 1 1 X^2+X X 1 0 1 1 X^2 1 1 X^2 0 X X 1 0 0 1 X 1 1 1 1 X 1 1 X^2 1 X^2 1 1 1 1 1 1 X^2+X X 1 1 X X 1 X^2+X 1 X^2 1 1 1 1 1 X^2 1 1 1 0 1 X 1 1 0 1 1 1 X^2+X 0 1 X 0 1 1 X^2+X 0 0 1 0 0 X X X^2+X 0 1 X^2+1 1 X^2+X+1 X+1 1 1 X^2+X 0 X+1 X+1 0 1 1 X X^2 X 1 X 1 X X^2+1 1 1 1 1 X X X^2 X+1 0 X^2 X X^2+X+1 X^2+X+1 X^2+X X 1 X^2+X 1 1 X^2+X+1 X X^2+X 1 1 X^2 X^2 1 X^2+1 X^2+1 X^2+X 1 0 1 X^2+X X X^2+X X^2+1 X+1 X^2+1 0 1 X+1 X^2+1 X^2+X+1 X^2+X X^2+1 1 X X^2 1 X^2+1 0 X^2+1 1 1 X^2 X^2 0 X^2+X X 1 1 0 0 1 0 X X^2+X+1 X^2+X+1 1 X+1 0 X X 1 X^2+1 X^2+1 X^2 1 X+1 X^2+X+1 X^2+1 X^2+X X+1 X^2+X X 1 X 1 X^2+X X^2+X X^2+1 X^2+X+1 X X^2 1 1 X^2+X 1 X^2+X 1 X^2+X X^2+X+1 X X+1 0 X^2 X^2+1 1 X X^2 X^2+X+1 X^2 X^2+X+1 0 X+1 0 1 0 X^2 X+1 1 1 X+1 X^2+X X 1 X+1 X X X+1 X+1 X+1 X^2+1 0 0 1 1 1 X^2 X^2+X X^2+X X^2+X+1 X^2+1 X^2+X+1 X+1 0 X^2+X X^2+X X X+1 X 1 0 0 0 0 1 X+1 X^2+X+1 X 1 X X+1 X+1 X^2+X 1 X^2+1 X 0 X^2+X+1 X^2 X^2+1 X+1 X^2+X X^2+X 1 X^2+X+1 X^2+X X^2+1 X^2+X X^2+1 X^2 1 X^2+1 X^2+X 1 0 X^2 1 X X^2+X+1 X^2+1 0 X^2+1 0 X^2+X+1 1 X+1 0 X+1 1 0 X^2 1 X^2+X+1 X^2+X+1 0 X X^2 X+1 X X^2+1 X^2+X+1 1 X^2+X+1 X+1 X^2 0 1 0 1 X^2+X X^2 X^2+X+1 X^2+X 1 1 X^2+X X^2+1 X^2+X X+1 X 0 X+1 X^2+X+1 X^2 1 X^2+X X+1 1 1 X^2+1 1 X^2+1 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+90x^84+376x^85+460x^86+640x^87+521x^88+768x^89+583x^90+724x^91+576x^92+678x^93+455x^94+450x^95+313x^96+420x^97+249x^98+278x^99+188x^100+150x^101+94x^102+94x^103+31x^104+24x^105+14x^106+6x^107+7x^108+1x^110+1x^116 The gray image is a linear code over GF(2) with n=368, k=13 and d=168. This code was found by Heurico 1.16 in 5.15 seconds.