The generator matrix 1 0 0 0 1 1 1 X+2 X^2+X 1 1 X^2+X 1 1 0 1 1 1 X^2+2 1 2 1 1 1 X 1 X X^2+X X^2+X+2 X^2+2 1 1 2 X+2 X+2 0 1 X^2+2 1 0 X^2 X^2+2 X 1 1 1 1 1 X^2+X+2 1 1 X^2 X^2 1 1 1 1 X 1 1 1 X^2+2 1 X^2+2 1 X^2+X+2 X^2+X+2 2 1 1 X^2 1 0 1 1 1 1 X+2 1 X^2+X+2 X^2 1 X 1 1 X^2 1 X+2 1 2 X+2 X^2+X X^2+X 0 1 0 0 2 X^2+3 X+3 1 0 X^2+2 X^2 1 X+1 X^2+X+1 1 1 2 X^2+2 2 2 1 X^2+1 X^2 1 1 3 1 1 X^2+X X X+2 X^2+3 1 X^2+2 1 X^2+X+2 X^2+1 1 X^2 0 1 1 X^2 X^2+3 X+2 X X^2+X X^2+X+2 1 X+1 X+3 X^2+X 1 X^2+2 0 X^2+X+3 X^2+X+2 1 X+3 1 X^2+1 1 X^2+3 X^2+X 1 1 1 1 1 X^2+1 X^2+X+2 X^2 1 X^2+X+2 X^2+X+2 2 X+2 2 X^2+1 1 1 X^2+X+1 X+2 X^2+3 X 1 X^2+X+3 1 1 X^2+X+2 X X+2 1 0 0 1 0 X^2+2 2 X^2 X^2 1 X^2+X+1 1 X+1 X^2+1 X^2+X+3 X^2+3 X+3 X^2+1 X+1 1 X^2+X+2 X^2+X+1 X^2+X+1 X^2 X^2 X^2+X X+2 X^2+X+2 X^2+1 X^2+X+2 1 1 1 X^2+X+1 1 X^2+1 X X+2 X^2 X 1 X^2+2 1 1 X+3 X^2+2 X+1 X X^2+2 X^2+X+1 0 X^2+X+2 2 X^2+X X^2+1 X+3 1 X^2+X+2 X^2+1 X+1 X^2 X^2+3 X+2 X+2 1 X^2+X X+3 X^2+X+1 X^2+X X^2+3 X^2+X+3 1 1 X^2+X X^2 X^2+X+2 X^2+3 X^2 X^2+2 X^2+X+3 2 2 0 1 X X^2+X+1 X+3 X+3 X^2+3 X^2+X+1 1 1 X^2+2 X+3 0 0 0 1 X^2+X+1 X^2+X+3 2 X+1 X^2+1 X+1 0 X+1 3 X^2+X X+2 X^2+X+3 X^2+3 X^2+X+2 X+3 1 X^2+1 X+2 X X^2+X X+3 X^2+1 0 X^2+2 1 X^2+2 2 X+3 X^2+X+1 X^2 X^2+X+2 1 0 X^2+X+2 X^2+X+3 X^2+X X^2+X+1 X^2+1 X+3 2 X^2+3 X+1 X^2+X+1 X^2+2 X^2 X+1 X^2+X+1 1 X^2+1 X^2+X 1 3 X^2+X X^2+X+1 X+3 X^2+2 X^2+X X^2+2 X^2+X+3 X+3 X 3 X X^2+X 1 X^2+3 X^2+2 X^2 X^2+X+1 X+1 2 X^2+X+3 X+2 1 X+3 X^2+1 3 X^2+1 X^2+X+1 X+3 X^2+3 2 X^2+3 2 3 1 3 1 X+2 generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86. Homogenous weight enumerator: w(x)=1x^0+756x^86+2014x^87+3670x^88+4558x^89+5549x^90+6090x^91+6997x^92+7012x^93+7264x^94+6382x^95+5118x^96+3750x^97+2752x^98+1610x^99+1036x^100+424x^101+309x^102+132x^103+69x^104+16x^105+9x^106+12x^107+5x^108+1x^110 The gray image is a code over GF(2) with n=744, k=16 and d=344. This code was found by Heurico 1.16 in 148 seconds.