The generator matrix

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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+288x^89+1077x^90+1618x^91+2468x^92+2838x^93+3243x^94+3604x^95+3871x^96+3066x^97+3128x^98+2378x^99+1966x^100+1178x^101+843x^102+556x^103+318x^104+134x^105+74x^106+48x^107+23x^108+24x^109+10x^110+4x^111+8x^113+1x^114+1x^116

The gray image is a linear code over GF(2) with n=768, k=15 and d=356.
This code was found by Heurico 1.16 in 23.2 seconds.