The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 X 1 X^2 1 X X^2 X 1 2 1 1 1 X^2+2 1 0 1 X 2 1 0 1 2 1 2 1 X 0 1 0 X 0 X 0 2 X+2 X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X+2 0 X^2+2 X X^2+X+2 X 0 2 X+2 X^2+X X^2 X^2 X^2+X X+2 0 X^2+X+2 X^2+2 X X^2 X^2+X+2 2 X^2 X^2 X+2 X+2 2 X+2 0 X+2 X X^2+X X^2+X+2 X^2+2 X^2+X X^2+X+2 0 0 X+2 0 X^2 X^2+X+2 X^2+X 2 2 X^2+2 X X^2+2 X^2 X+2 X+2 X^2+X+2 X^2+X X X^2+X+2 X+2 X X^2+X+2 X^2+X X X+2 X 2 X X 0 X+2 X X 2 X X^2+X X X 0 X^2+2 X^2 X X^2 0 0 X X X^2+2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2 X 0 2 X^2+X+2 X+2 X^2 0 X+2 X X^2 X^2+X+2 X X^2+2 X^2+2 X^2+X+2 0 X^2+X 2 2 X^2+X X+2 X^2+2 X^2+X X X^2+2 X^2+2 0 X^2+X+2 X X^2+2 X 2 0 X+2 X^2+2 X^2+X+2 X^2+2 X^2+X+2 0 0 2 X^2 X^2+X X^2+X+2 0 X+2 X+2 X+2 X^2+X+2 X X^2 X^2 X^2 2 X^2 X X^2+X+2 X X^2+X+2 X^2+X X^2+2 X^2 X^2+X X+2 X+2 X^2+X+2 X^2 2 X+2 X X^2+2 X^2 X^2+X X^2+X X^2+X+2 X+2 X X+2 X 2 X^2+X+2 X^2+2 X^2 0 0 0 2 0 0 2 0 2 0 2 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 0 0 2 0 2 2 2 0 0 2 2 0 2 2 0 2 0 0 0 2 0 2 2 0 0 2 0 2 2 0 2 2 0 0 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 2 0 2 2 2 0 0 2 2 2 0 0 0 0 2 2 0 2 0 0 0 0 0 2 2 2 2 2 0 0 2 2 0 2 0 0 2 2 0 0 0 2 0 2 0 2 2 0 2 0 2 0 2 2 2 0 0 0 0 0 0 2 2 2 2 0 2 2 2 0 2 0 0 2 2 0 0 2 0 0 generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 87. Homogenous weight enumerator: w(x)=1x^0+116x^87+193x^88+336x^89+272x^90+476x^91+469x^92+560x^93+432x^94+424x^95+267x^96+212x^97+84x^98+116x^99+46x^100+40x^101+8x^102+12x^103+10x^104+4x^105+4x^106+8x^107+5x^108+1x^152 The gray image is a code over GF(2) with n=744, k=12 and d=348. This code was found by Heurico 1.16 in 1.38 seconds.