The generator matrix

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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+152x^90+1098x^91+2437x^92+3186x^93+4414x^94+5406x^95+6457x^96+6466x^97+7144x^98+6952x^99+6094x^100+4890x^101+3981x^102+2674x^103+1975x^104+1040x^105+587x^106+326x^107+119x^108+56x^109+29x^110+20x^111+9x^112+10x^113+1x^114+4x^115+4x^118+4x^120

The gray image is a linear code over GF(2) with n=784, k=16 and d=360.
This code was found by Heurico 1.16 in 56.3 seconds.