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

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+312x^93+325x^94+420x^95+171x^96+300x^97+211x^98+148x^99+52x^100+68x^101+6x^102+24x^103+8x^109+1x^118+1x^154

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 0.765 seconds.