The generator matrix

 1  0  0  0  1  1  1  1  2  1 X+2 X^2+X+2  1 X^2+X  1  1  1  1 X^2+2  X  1 X+2 X^2+X  1  2  1  1 X^2+X  1  1 X+2 X^2+2  2 X^2+X+2  1 X^2+2 X^2  1  1  1  1  X  2  1  2 X^2+X X^2+X  0  1 X^2+2  1  1 X^2+X+2 X^2+2  1  1  1 X^2+X+2 X^2+2  1  1  1  1  1  1  1  1  1  1 X^2+2  0 X^2  X X^2  1  1 X+2  1  1  X  1  1  1  0 X^2  2  1 X^2+X+2 X^2  X X+2  1  1  1  1  1  X  1
 0  1  0  0  X X^2+1  2 X^2+3  1 X^2+X+2  X  1  3  1 X^2+X+3 X+2  1 X^2+X+1  1  2 X+3 X^2+2  1 X^2+X+3  1 X^2+X  2  1 X^2+X X^2+X+3 X^2+2  0  2  1  2  1  1 X^2  3 X^2+X  3  X X^2+X+2 X+2  1 X^2+X+2 X^2+2  1  3  1 X^2+X+1 X^2+X+3  1  1 X^2+2  0 X+1  1  0 X^2 X^2 X^2+3  3  X X^2+3  1 X^2+X+2 X^2+X+3 X^2 X^2+X+2 X^2+2 X^2+2  1  1 X^2+1 X+3  1 X+1 X^2+2  1 X^2+2 X+3 X^2+1  1  1 X^2+X+2 X+3  1 X+2 X^2+X+2  1 X+2 X^2+X+1 X^2+X+3 X^2+2 X^2+X+2  1  2
 0  0  1  0  0  2 X^2+3 X^2+1  1 X^2+1  1  3 X^2+X+2 X+2  3  0 X^2+X+1 X^2 X+1  1 X^2  2 X^2+1 X+3  2 X^2+X+3 X+2 X^2+X+2  3 X+1  1  1 X^2+X+2 X^2+X+1  1  1 X^2+X  1  2 X^2+X+2 X^2+X+3  1  1  2 X^2+X X^2+2  1  3 X^2+3 X^2+2  X  X X+2 X^2+X+2 X^2+X+3 X^2+X+2  0  3  1  0  1 X^2+X+1 X^2+X+2 X^2+X+2 X^2+3 X^2+1  2 X^2+1 X^2+3  1 X^2  1 X^2+X+3 X^2+2 X+3 X+1 X^2+2  X X^2+X  2 X^2+1 X+3 X+1 X^2 X+3  0  1 X+3  1  1  3  X  2 X+2 X^2+X  3 X^2+2  0
 0  0  0  1  1 X+3 X+1  2 X^2+X+3 X+2 X^2+X+1 X^2+X+2 X^2+X X+3 X+1 X^2+X+3 X+1 X^2+X X^2+X+2 X^2+1  3  1 X^2+3  X  1  X  X  0  1 X^2 X^2+X+2 X+1  1 X^2 X^2+X+2 X^2+1 X+3 X^2+3 X^2+1 X^2+X+3 X^2+X+1 X^2+X X+3  0  0  1 X^2 X+2  3 X+1  2 X^2+X+1 X^2+X X^2+1 X^2+3 X^2+X+3 X^2+X X+1  3 X^2+X+2  0  3 X^2+1 X^2+2 X^2+X X+3 X^2+X+3 X^2+X+3 X^2+2 X^2+X  1 X+1 X^2+X+3 X^2+X X+2 X^2+X  0  X X^2+3  3 X+2 X^2+1 X^2+X+2  3  3  1  X X+2  2  0 X+2 X^2+X+2 X^2+X+3 X^2+3  X X^2 X+1 X^2
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  2  0  0  2  0  0  0  2  0  0  0  2  2  0  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  0  0  0  2  2  2  0  0  2  2  0  0  2  2  2  2  0  2  2  0  0  2  0  0  2  0  2  2  0  2  0

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+104x^89+1051x^90+2512x^91+3821x^92+5746x^93+8547x^94+11000x^95+11959x^96+13996x^97+13838x^98+14192x^99+12847x^100+10610x^101+8132x^102+5304x^103+3058x^104+2144x^105+1196x^106+554x^107+236x^108+98x^109+63x^110+30x^111+12x^112+4x^113+5x^114+6x^115+2x^116+2x^117+2x^119

The gray image is a code over GF(2) with n=784, k=17 and d=356.
This code was found by Heurico 1.16 in 226 seconds.