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 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 0 1 X 1 1 X 1 X 1 X 2 0 1 X X^2+2 1 1 1 1 1 1 0 1 X^2+2 1 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+2 0 X+2 X+2 2 X+2 X^2+X X^2 X^2 X X^2+X+2 0 X^2+X 2 0 X^2+X X^2+X+2 X 2 X^2+X+2 X 0 X X^2+X+2 X X^2+2 X^2 X^2+2 X+2 X^2+2 X^2+2 X^2+X+2 2 2 X 0 X+2 X^2 0 X+2 X^2+2 X^2+X X+2 X^2+X+2 X^2+X X X 0 0 2 X^2 X^2+X X^2+X 0 2 X^2+2 X 2 0 X X^2+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^2+X+2 X 0 0 X^2 X^2+X X^2+X+2 2 0 X^2+X X^2+X+2 2 X^2 0 X 2 X^2 X+2 X^2 X X+2 X^2+2 X+2 X^2+X X^2+2 X^2+2 X+2 X^2+2 X X X^2+2 X^2+X+2 X^2+X+2 X+2 X X^2 X X X^2+X X^2+X+2 X 2 X^2 X^2+X X 0 X^2+X+2 X+2 X X X^2 X^2+X+2 X+2 X X^2 X^2+X X^2+X X X+2 X^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 2 2 0 2 2 2 2 0 2 0 0 0 2 2 2 2 0 0 2 0 2 2 2 0 0 0 0 0 2 0 2 0 0 2 2 0 0 0 2 0 2 0 0 0 0 2 0 2 0 2 2 0 0 2 0 2 0 2 0 2 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 0 2 2 0 0 2 2 2 2 2 0 0 2 0 2 0 0 0 0 2 2 2 0 2 0 2 0 2 2 2 0 0 0 0 2 2 2 2 2 2 0 0 2 0 0 0 2 0 0 2 2 0 0 0 0 2 2 0 2 0 0 generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 92. Homogenous weight enumerator: w(x)=1x^0+123x^92+178x^93+279x^94+330x^95+399x^96+610x^97+431x^98+628x^99+304x^100+242x^101+227x^102+122x^103+75x^104+42x^105+51x^106+20x^107+25x^108+2x^110+4x^111+2x^114+1x^168 The gray image is a code over GF(2) with n=784, k=12 and d=368. This code was found by Heurico 1.16 in 1.61 seconds.