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+2 X^2 1 2 X 1 X^2+X+2 1 0 X+2 X^2+2 X^2 1 1 X^2+2 1 1 X+2 2 X+2 2 1 1 1 1 1 X^2+2 0 1 1 0 1 1 1 X^2+X 1 X^2+X X^2+X 1 1 X X+2 1 1 1 1 1 2 1 X^2 1 X^2+2 X 1 X^2+X+2 1 X 1 1 1 1 X^2+2 1 1 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 X^2+X 1 X^2+X X^2+X+2 1 3 X+2 X+3 X+2 1 1 1 X^2+X X 1 X+2 1 1 1 X^2 X^2 X^2+2 X+3 X^2+X X+1 1 X^2+X X^2+X+2 X^2+X+3 X^2 X+2 X^2+X+1 3 X 1 X+2 1 2 X X^2+X+1 1 1 X+2 X X+2 1 X 1 X^2+X+3 X^2+2 X 1 X X^2+X+1 X X^2+X+2 1 X+3 X^2 0 X^2+3 1 X^2+X+3 X^2+X+2 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+X+2 1 X+1 1 X^2+X+1 3 1 2 2 X^2+2 X^2 X^2+1 3 X^2 X X^2+X+2 X^2 X^2+X+1 3 1 1 X X X^2+1 X^2+X+2 X^2+1 1 1 X^2+X+1 X+1 1 X X^2+X+3 X^2+X X^2+1 X+1 X^2+X X^2 X^2+2 1 X+2 X+3 3 X^2+1 X^2+X+1 X 0 X^2+X+3 X^2+X+2 X 2 X^2+2 1 X^2+2 1 X^2+2 X^2+2 X^2+X X^2 X+3 X+2 0 X^2+3 X 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 1 2 X^2 X^2+3 X^2+X+2 X^2+X X^2+X+2 X 1 1 X+2 1 X+3 X^2+X+3 X^2 X+1 X^2+2 X^2 X^2+X+1 X+3 X^2+X X+2 X+3 X^2+3 X^2+X+2 X^2+X+1 X+3 X^2+X+2 X^2+X+3 2 2 X^2+2 X^2+2 X^2+1 0 X+3 X^2+2 1 X+2 2 X^2+1 X^2+3 X^2+2 X^2+X+2 0 X+1 1 X^2 X^2+1 1 X^2 3 0 X+1 X+3 X+3 X^2+X X^2+X+1 X^2+1 X^2+3 X^2+3 X^2+X+2 X+3 X^2 generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+796x^84+1960x^85+3118x^86+4550x^87+5874x^88+6384x^89+7566x^90+7080x^91+6637x^92+5748x^93+5539x^94+3974x^95+2785x^96+1732x^97+948x^98+432x^99+189x^100+116x^101+77x^102+8x^103+6x^104+12x^105+4x^107 The gray image is a code over GF(2) with n=728, k=16 and d=336. This code was found by Heurico 1.16 in 60.4 seconds.