The generator matrix

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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+92x^87+1008x^88+2056x^89+4048x^90+5752x^91+8750x^92+10256x^93+12722x^94+13784x^95+14613x^96+14170x^97+12975x^98+10106x^99+8070x^100+5180x^101+3703x^102+1732x^103+1098x^104+436x^105+247x^106+142x^107+68x^108+28x^109+15x^110+6x^111+8x^112+2x^113+2x^114+2x^119

The gray image is a linear code over GF(2) with n=768, k=17 and d=348.
This code was found by Heurico 1.16 in 234 seconds.