The generator matrix

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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+104x^89+1209x^90+2496x^91+4370x^92+5558x^93+8633x^94+9546x^95+13096x^96+13360x^97+14820x^98+13392x^99+13431x^100+9376x^101+8504x^102+5168x^103+3792x^104+1926x^105+1161x^106+644x^107+283x^108+64x^109+65x^110+46x^111+1x^112+10x^113+7x^114+4x^115+2x^116+2x^117+1x^122

The gray image is a linear code over GF(2) with n=784, k=17 and d=356.
This code was found by Heurico 1.16 in 240 seconds.