The generator matrix 1 0 0 0 1 1 1 X+2 X^2+X 1 1 1 1 X^2+X X 0 1 1 X^2+2 1 1 1 X^2 X+2 1 X+2 1 X^2 X^2 X+2 X^2 1 1 1 1 1 X^2 1 0 X+2 1 1 1 X+2 2 1 X+2 1 X+2 1 1 X^2+2 X^2 1 X^2+X+2 1 1 X^2+2 2 X^2 1 1 X^2 1 X^2+X+2 X^2 1 1 X+2 1 1 X 1 X+2 X 1 1 1 X^2 1 1 X 1 1 1 X^2+2 1 1 1 1 1 1 1 1 1 X+2 1 0 1 0 0 2 X^2+3 X+3 1 0 X^2+2 X^2 X^2+X+3 X^2+1 1 1 X+2 1 X^2+X+3 1 X^2+X X^2 X+2 1 X X^2 1 X^2+X+2 X^2 1 1 2 X^2+X+1 X^2+X+1 X^2+2 X^2+X X+1 1 X 1 X^2+X 2 X^2+1 1 1 1 X^2+3 X^2+X+2 X+3 2 X^2+X+3 X^2+3 X^2+X+2 1 X+1 1 X^2+X+1 X+1 1 2 1 2 X^2+X X^2+X X^2+1 1 1 X+2 X^2+1 X^2 X^2+2 X^2+X+2 1 X X^2+2 1 X^2+3 X^2+2 X^2+X+3 1 X+3 3 X 3 X^2+X+2 X^2+X+2 X^2+2 3 X^2+3 0 X+2 X X^2+X X^2+2 X+2 X^2+X+1 X^2+X+2 0 0 0 1 0 X^2+2 2 X^2 X^2 1 X^2+X+1 1 X+3 3 X^2+1 3 1 X+3 X 0 X+2 X^2 X+1 X^2+X+3 1 X^2+3 0 X^2 X^2+X+2 X^2+1 X+1 1 X^2+X X+2 1 X^2+2 3 X+1 X+3 X^2 X+2 X+1 X^2+X X^2+1 X X^2+X+3 X+3 1 X+3 1 X+1 X^2+X 1 X X^2+3 X^2+1 2 X^2+X X^2+X+1 1 X^2+X+2 X^2+2 3 0 X^2+2 X^2 X^2+3 X^2+X+2 X+3 X+2 0 X^2+X+1 X^2+X+3 X^2+1 1 X^2+X+2 X^2+X+2 X+2 1 X^2+3 X+2 X^2+X+2 1 2 X+3 X^2+1 1 X^2+3 X^2+X+1 X^2+X 0 0 X^2+1 X^2+3 X^2 X^2+3 1 2 0 0 0 1 X^2+X+1 X^2+X+3 2 X+1 X^2+1 X+1 0 X+2 X^2+1 X^2+1 X^2+X+2 X^2+1 X^2+X+1 X^2+X X^2+3 X+1 X^2+X+2 X^2+2 X^2+X 0 X^2+1 X^2 X^2+X 1 0 X^2+3 X^2+X+3 X^2+X+1 X^2 X X^2+X+3 X^2+X+2 X^2+X+3 3 X+3 1 2 X+1 X^2+X+3 X^2 X^2+1 X+2 X^2+3 X^2+3 X X^2 3 X X^2+2 X^2 0 X X^2+1 2 1 X^2+X+2 X^2+3 X^2+3 1 X^2+2 1 3 X^2+3 X^2+X+1 1 X X+1 X^2+X X+2 X^2 X^2+X+1 X^2 1 X^2+X+1 X X+3 X+3 1 1 1 0 X+1 X^2+X X^2+1 X X^2+X X^2 X^2+X+3 X+1 X^2+1 2 X^2+X+1 0 generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 89. Homogenous weight enumerator: w(x)=1x^0+102x^89+1058x^90+2188x^91+3331x^92+4416x^93+5298x^94+6390x^95+7030x^96+7012x^97+7026x^98+5930x^99+5375x^100+3792x^101+2564x^102+1800x^103+1149x^104+568x^105+257x^106+142x^107+46x^108+24x^109+8x^110+10x^111+4x^112+6x^113+5x^114+4x^115 The gray image is a code over GF(2) with n=776, k=16 and d=356. This code was found by Heurico 1.16 in 54.9 seconds.