The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 1 0 1 1 X^2+X X^2+2 1 1 1 1 X+2 1 1 0 1 1 X^2+X 1 1 X^2+2 1 X+2 1 1 0 1 X^2+X 1 1 X^2+2 1 1 1 1 X+2 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 X 1 1 1 1 X 1 1 1 1 0 2 1 0 1 X^2+X X X^2+X+2 X 1 1 1 X+2 1 2 1 1 0 0 1 X+1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 X+2 1 3 X+1 0 1 X^2+X X^2+1 1 1 X^2+2 X^2+X+3 X+2 3 1 0 X+1 1 X^2+X X^2+1 1 X^2+2 X^2+X+3 1 3 1 X+2 X^2+X 1 X+1 1 0 X^2+1 1 X^2+2 X^2+X+3 X+2 3 1 0 X^2+X+2 2 X 0 X^2 X^2+X 2 X^2+X+2 X^2 X^2+X+2 X^2 X+2 2 X^2+2 X^2+2 X^2+X X+2 0 X+2 2 X^2+X X^2 X+1 X+1 1 1 0 1 X+3 1 1 1 X^2+X+2 X^2+X+2 X^2+1 X^2+3 1 2 X X^2+X X^2+X+1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 0 2 2 2 2 0 2 0 0 0 0 2 0 0 0 2 2 0 0 2 2 2 0 0 2 0 2 2 2 2 0 2 2 2 0 0 0 2 0 0 2 2 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 0 2 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 2 2 2 0 0 2 0 2 2 0 0 2 0 2 0 2 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 2 0 2 0 0 0 2 2 2 0 0 0 0 2 0 0 2 0 0 0 2 2 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 2 0 2 2 2 0 2 0 0 0 2 2 0 0 2 2 2 2 0 2 0 0 0 2 2 2 0 0 0 0 2 0 2 2 2 2 0 0 0 0 2 2 0 0 0 2 2 2 0 0 2 0 0 0 2 2 0 2 2 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 2 0 2 0 0 2 0 0 2 0 2 0 0 2 0 0 2 2 2 2 2 0 2 2 0 2 2 0 2 2 2 0 2 0 0 2 0 0 0 0 2 0 2 2 0 0 2 2 0 0 2 2 0 0 0 0 0 2 2 0 0 2 0 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+276x^86+224x^87+528x^88+240x^89+583x^90+608x^91+459x^92+256x^93+382x^94+192x^95+206x^96+16x^97+101x^98+20x^100+1x^102+1x^124+1x^126+1x^128 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 seconds.