The generator matrix 1 0 1 1 1 X^2+X 1 X^2+2 1 1 1 X+2 1 1 2 1 X^2+X+2 1 1 X^2 1 X 1 1 1 1 1 X^2+2 1 1 X^2+X 1 1 X^2+X+2 1 0 1 X 1 1 1 1 2 X 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 1 X 1 1 1 X 1 1 1 1 1 1 1 1 X 1 0 1 X^2+X+2 2 1 X^2+2 1 0 1 X+1 X^2+X+2 X^2+3 1 X 1 X^2+X+1 2 1 1 X^2 X+1 1 X^2+1 1 X^2+2 X^2+X+3 1 3 1 0 X^2+2 X^2+X X+2 X+1 1 X+2 X^2+1 1 X^2+X X+3 1 3 1 X^2+X 1 2 1 X^2+X+3 X^2+2 1 1 X^2+3 X+2 X^2+2 X^2+X+1 1 0 X^2+X+2 X^2+X 0 0 X+2 X^2 X+2 X^2+2 X X+2 0 X^2+2 0 1 X^2+X X+1 X^2+1 X^2+2 X^2+X 1 X^2+X+2 X^2+X 0 X^2+2 X+2 2 X^2+X+1 X^2+X+3 X^2+X+2 X^2+1 X^2+1 X^2+3 1 2 1 X^2+X+2 1 1 3 1 0 0 0 X^2 X^2 X^2+2 0 X^2+2 0 X^2 X^2 X^2+2 0 X^2+2 2 X^2 2 X^2 0 2 X^2 2 X^2 0 0 0 2 2 0 0 2 0 0 X^2 X^2 2 0 X^2+2 X^2+2 X^2+2 X^2 2 0 X^2 0 X^2+2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2 X^2 X^2 0 2 X^2 0 X^2+2 X^2+2 X^2+2 0 2 2 X^2 2 X^2 X^2+2 0 2 X^2 X^2 X^2+2 X^2+2 2 0 X^2+2 X^2 X^2+2 2 0 2 0 X^2+2 2 2 X^2+2 2 0 0 2 2 0 0 0 2 0 2 2 2 2 0 2 0 0 2 0 2 0 0 0 2 0 2 2 2 0 2 0 0 2 0 0 0 0 2 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 0 0 0 2 2 0 2 0 2 0 2 2 0 2 0 0 0 2 0 0 2 2 2 2 0 0 0 0 2 0 2 2 2 2 0 2 0 0 0 2 2 2 0 0 2 2 2 0 0 0 2 2 0 0 0 2 2 0 0 0 0 2 2 0 2 2 2 2 0 2 0 2 0 0 0 2 2 0 2 0 2 2 2 0 2 0 2 2 0 0 2 0 2 0 2 2 0 0 2 2 2 0 0 2 0 0 0 2 2 2 0 2 2 0 0 generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+182x^86+356x^87+483x^88+338x^89+458x^90+594x^91+408x^92+300x^93+465x^94+264x^95+126x^96+62x^97+43x^98+2x^99+5x^100+2x^101+1x^102+2x^109+2x^110+1x^130+1x^132 The gray image is a code over GF(2) with n=728, k=12 and d=344. This code was found by Heurico 1.16 in 1.17 seconds.