The generator matrix

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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+322x^93+337x^94+308x^95+324x^96+214x^97+251x^98+134x^99+42x^100+80x^101+2x^102+22x^103+1x^106+8x^109+1x^118+1x^152

The gray image is a linear code over GF(2) with n=768, k=11 and d=372.
This code was found by Heurico 1.16 in 2.42 seconds.