The generator matrix 1 0 1 1 1 X^2+X 1 X^2+2 1 1 1 X+2 1 1 2 1 X^2+X+2 1 1 1 X^2 1 1 X 1 1 0 1 X^2+X 1 1 0 1 X 1 1 1 X^2+2 1 1 X 1 X^2+2 1 X^2+X 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X^2 1 1 X^2+2 1 1 1 1 1 1 1 1 1 2 0 1 1 1 X+2 1 1 1 0 X+2 0 1 X+1 X^2+X X^2+1 1 3 1 X^2+2 X+1 X+2 1 X^2+X+3 2 1 X^2+X+2 1 X^2+3 X^2+X+1 X^2 1 X 1 1 0 X+1 1 X^2+X 1 X^2+X+3 X^2+3 1 2 1 1 X+2 X^2 1 X^2+X+1 X^2+X+2 1 X^2+3 1 X+3 1 1 X^2 X X X^2 2 X^2+X X^2+X X^2+2 2 X 2 X^2 X^2+X X X^2+2 X^2+X X^2 X^2+X+2 X^2+2 X^2+1 X+1 X+3 X+1 X^2+3 X^2+X+2 3 X^2+X+1 1 X 2 X^2+X+1 X X^2+X+1 X^2+X+1 X^2+1 3 X^2+1 3 X^2+X+1 X+1 X^2+X X 1 X+2 X^2+X+3 X^2+X+2 1 X+1 X^2+X+3 0 1 1 0 0 X^2 0 0 2 0 2 2 2 2 0 2 X^2 X^2+2 X^2+2 X^2 X^2 X^2+2 X^2 X^2+2 X^2+2 X^2+2 X^2 0 2 0 0 0 2 X^2 X^2+2 X^2 X^2 X^2+2 0 X^2+2 2 X^2+2 X^2+2 2 0 X^2+2 X^2 X^2 0 X^2 X^2+2 2 2 2 2 X^2+2 2 X^2+2 X^2+2 0 0 0 X^2 X^2 X^2 X^2 2 0 0 0 X^2+2 X^2+2 X^2+2 2 2 2 X^2+2 X^2+2 2 2 0 X^2 X^2 2 X^2 X^2 0 0 2 0 X^2 0 X^2+2 X^2+2 X^2 0 0 0 X^2+2 X^2 X^2+2 0 0 0 2 0 2 2 0 2 2 0 2 0 0 2 2 0 2 2 2 2 0 0 0 0 2 2 2 0 0 0 0 2 2 2 0 2 2 0 0 0 2 0 2 2 0 0 2 2 0 0 2 2 2 0 0 2 2 0 2 0 0 2 0 2 0 0 2 0 0 0 2 2 2 2 2 2 2 0 2 2 0 2 0 0 0 0 2 2 2 2 2 2 0 2 2 0 2 0 0 0 0 2 2 2 2 2 0 2 0 0 2 0 2 0 2 0 0 2 0 2 2 2 2 2 2 2 2 0 2 0 2 0 0 2 0 2 0 0 0 0 2 0 0 2 2 0 0 2 2 0 0 0 2 2 2 2 0 0 2 2 0 0 0 2 0 0 2 2 0 2 2 0 2 0 0 2 2 2 0 0 2 0 0 0 2 0 0 2 2 2 0 0 2 0 0 generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 93. Homogenous weight enumerator: w(x)=1x^0+188x^93+435x^94+388x^95+383x^96+458x^97+622x^98+368x^99+346x^100+308x^101+279x^102+140x^103+87x^104+62x^105+6x^106+12x^108+4x^109+3x^112+1x^114+4x^121+1x^146 The gray image is a code over GF(2) with n=784, k=12 and d=372. This code was found by Heurico 1.16 in 1.53 seconds.