The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3  X X^2  X X^3  X X^2  X  0  X X^3+X^2  X X^3  X X^2  X X^3+X^2  X X^2 X^2  X X^3  X X^3+X^2  X  0  X X^2  0  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X  0 X^3+X^2+X X^2  X X^3+X^2+X  0  0 X^2+X X^3+X X^2 X^3+X^2  X  0 X^2+X  0 X^3+X^2+X X^2  X X^3+X^2 X^3+X X^3+X X^3 X^3 X^3+X X^3+X^2 X^3+X^2+X X^2 X^2+X X^3 X^3+X^2+X X^2  X X^3 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^2+X X^3+X^2 X^3+X X^2+X  X X^3+X  X X^2+X  X X^3+X  X X^3+X^2+X  X  X  X X^2+X  X X^3+X  X X^2+X  X X^3+X^2+X  X X^3 X^3+X  X X^3+X^2+X  X  X  X  X X^3  X  0 X^2
 0  0 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^2  0 X^3+X^2  0  0 X^3+X^2  0 X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3  0 X^3 X^2 X^3+X^2 X^3+X^2 X^3  0 X^2  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2  0  0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3  0  0 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2  0  0 X^2
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  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+176x^93+90x^94+176x^95+202x^96+144x^97+84x^98+112x^99+2x^100+2x^102+32x^103+1x^120+1x^124+1x^132

The gray image is a linear code over GF(2) with n=768, k=10 and d=372.
This code was found by Heurico 1.16 in 1.5 seconds.