The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+154x^89+1125x^90+2480x^91+4355x^92+5704x^93+8481x^94+9820x^95+13017x^96+13174x^97+14799x^98+13456x^99+12922x^100+9990x^101+8437x^102+5378x^103+3611x^104+1992x^105+1189x^106+450x^107+337x^108+60x^109+36x^110+22x^111+29x^112+28x^113+13x^114+8x^115+2x^117+2x^123

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 239 seconds.