The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+104x^89+1056x^90+2448x^91+3889x^92+5936x^93+8504x^94+10412x^95+12243x^96+13964x^97+14460x^98+13820x^99+12804x^100+10556x^101+7914x^102+5324x^103+3673x^104+1968x^105+926x^106+616x^107+199x^108+108x^109+62x^110+16x^111+33x^112+4x^113+22x^114+4x^115+3x^116+2x^120+1x^124

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 243 seconds.