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

generates a code of length 99 over Z2[X]/(X^4) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+134x^91+1022x^92+2220x^93+3412x^94+4784x^95+5259x^96+6196x^97+6464x^98+7246x^99+6682x^100+6504x^101+4990x^102+3872x^103+2724x^104+1852x^105+1016x^106+564x^107+340x^108+116x^109+60x^110+20x^111+16x^112+24x^113+8x^114+4x^115+2x^118+4x^120

The gray image is a linear code over GF(2) with n=792, k=16 and d=364.
This code was found by Heurico 1.16 in 55.8 seconds.