The generator matrix 1 0 1 1 1 X^3+X^2+X 1 1 X^3 1 1 X^2+X X^2 X^3+X 1 1 1 1 X 1 1 X^3+X^2 1 1 X^3+X X^3 1 1 X^3+X^2+X 1 1 X^3+X 1 1 X^2 1 1 X^2 1 0 X^3+X^2+X 1 1 1 X^3+X^2+X 1 0 1 1 1 0 X X 0 X^3+X^2 X^3+X X^3+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3 X^3+X^2 X^3+X X^2+X X^2+X X X X^3 X^3+X^2+X X^3 1 1 1 1 1 1 1 X^3+X^2 1 X X^3+X^2+X 1 X X^2+X 1 X 0 X 1 0 1 X+1 X^3+X^2+X X^2+1 1 X^3+X^2+1 0 1 X^3+X^2+X X+1 1 1 1 X^3 X^2+1 X^3+X X^3+X+1 1 0 X+1 1 X^3+X X^2+1 1 1 X^2 X^3+X^2+X+1 1 1 X 1 X^2+X+1 X^2+X 1 X^3+X^2 1 1 X^2 1 1 X^3+1 X^3+X^2+X X^2+X+1 1 1 1 X^2 X^3+X X^2+X+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^3 1 1 1 X+1 X^3 X^2+1 X+1 X^2+X X^3+X^2+X+1 1 1 X^3+X^2 X^3+X^2+X 1 X^3+X^2+1 X^3+X^2+X 1 X^2 X^3+X^2+X 1 X^3 X+1 0 0 X^2 0 0 0 0 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^3 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3 0 X^2 X^3+X^2 0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 0 0 X^2 0 X^2 X^3 X^2 0 X^3+X^2 X^3 0 0 X^3 0 X^2 0 X^2 X^3+X^2 0 X^3 X^3 X^3+X^2 0 X^3+X^2 X^3+X^2 X^3 X^3+X^2 0 X^3 X^3 0 X^3+X^2 X^3+X^2 0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 0 0 X^3 0 X^2 X^3+X^2 0 0 0 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 0 X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 0 0 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^3 X^2 0 X^3+X^2 X^2 X^3 X^2 X^3 X^2 0 X^3+X^2 X^3+X^2 0 0 X^3+X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^3+X^2 X^2 X^2 0 X^3 X^3+X^2 0 X^3 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 0 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^2 X^3 generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+161x^84+354x^85+491x^86+478x^87+473x^88+342x^89+438x^90+386x^91+433x^92+310x^93+151x^94+26x^95+15x^96+18x^97+5x^98+6x^99+2x^108+2x^110+2x^112+1x^122+1x^128 The gray image is a linear code over GF(2) with n=712, k=12 and d=336. This code was found by Heurico 1.16 in 0.891 seconds.