The generator matrix 1 0 0 1 1 1 X X+2 1 1 1 X+2 1 X^2+2 1 1 X 1 X^2+X 1 X+2 1 X^2+X+2 1 X^2+2 X^2 1 1 1 X+2 1 X^2+X 1 1 1 X+2 1 X^2+2 1 X^2+X+2 X+2 X^2+X 1 1 1 1 1 1 X^2+2 2 X^2+2 1 1 1 1 X^2 1 X^2+X+2 1 X^2 1 1 1 0 1 1 X^2+X+2 1 1 X^2 1 X^2+X+2 1 1 X^2 1 1 X^2+X 1 0 1 X^2+X X X^2+2 1 1 1 1 1 X 1 0 1 0 0 X^2+1 X+1 1 2 0 2 X+3 1 1 1 X 0 1 X^2+1 1 X^2+3 X X^2 1 X^2+X+1 1 X^2+X X^2+X+2 X+3 3 1 X+2 1 X^2+X X^2+3 X^2+2 X 1 1 X+2 X^2+2 1 X^2 X+3 3 X X+2 X+3 2 X^2+X+2 1 1 1 0 X^2+X+1 X^2+2 1 X^2+1 1 X^2+1 1 X X^2+2 X^2+X 1 3 X^2+3 1 X^2+X+2 X^2+X+1 2 X^2+X+3 1 0 X+2 2 X^2+2 X+1 1 X^2+1 1 X^2+X+2 1 1 2 X^2+X+3 X^2+X 0 X^2+X+1 1 1 X^2+2 0 0 1 1 1 0 X^2+1 1 X X^2+X+3 1 X X^2+X X+3 X^2+X+1 X^2+X X+3 X^2 X^2+X X^2+3 1 X+1 1 0 X^2 1 X^2+X+2 X^2+1 X^2+2 X+3 X+3 X^2+2 2 X^2+X+1 X^2+1 1 X^2+X+2 1 0 1 2 1 X X^2+1 X+1 3 X^2 X 1 X^2+1 X X^2+X+3 X^2 X^2+X+3 2 X+2 X^2+2 X^2+2 X^2+X+3 X^2+X+1 X^2+1 2 X^2 X^2+3 X+2 X^2+X+1 3 X^2+X X^2+X+3 1 X^2+X X^2+1 X^2+X X^2+3 1 X^2+X+3 X X^2+X X+2 2 X X+2 3 1 3 X^2+1 3 X+2 0 X^2+X+1 0 0 0 0 X X+2 2 X+2 X+2 X+2 X 0 X X+2 2 X 2 X^2+X+2 2 2 X^2+2 X^2+X+2 X^2 0 X^2+X X+2 X^2+2 X^2+X+2 X+2 X 0 X^2+2 X^2+X+2 X X^2+X+2 X^2 X^2 X^2 X X^2 X^2+X+2 2 2 X 2 0 X+2 X^2+2 X^2+X+2 X^2+X+2 X^2 X^2+X 0 X^2+X X^2+X+2 X^2+2 X^2 X^2+X+2 X+2 X+2 X^2+X X^2+X X+2 0 X^2+X X^2+X+2 0 X^2+X X^2 X+2 X+2 0 X^2 X^2+X X^2 X^2+X X^2+X X^2+X+2 X^2 2 X X X^2+X X^2+X X X^2 X^2+2 X^2+X+2 X^2+X X^2 X^2 0 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+200x^84+920x^85+1669x^86+2358x^87+2770x^88+3470x^89+3644x^90+3988x^91+3355x^92+3122x^93+2263x^94+1804x^95+1330x^96+878x^97+457x^98+260x^99+142x^100+46x^101+21x^102+38x^103+9x^104+12x^105+9x^106+1x^108+1x^110 The gray image is a code over GF(2) with n=728, k=15 and d=336. This code was found by Heurico 1.16 in 14.8 seconds.