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  0  1  1  1  1  1 X^3  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  X  X X^2  0 X^3+X^2  X X^3 X^2  X  X  X  X  X X^2  X X^3+X^2 X^3  X X^2  0  0 X^3  X  X X^2  0  0  1
 0  X  0  X  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  0  0  X  X  0  0  X  X X^2 X^2 X^2+X X^3 X^2+X X^2 X^2 X^2+X X^2+X X^3 X^3 X^3 X^3+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3 X^3+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3 X^3+X X^3+X X^3 X^3 X^3+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X  X X^2+X  X X^3+X^2+X X^2  X  X X^2  X  X X^3+X^2 X^3+X X^3+X^2+X X^3+X X^2+X X^3+X^2  0  X  X X^3  X  X  0 X^2 X^3+X^2 X^3+X^2  0 X^2  X  0
 0  0  X  X X^3+X^2 X^2+X X^3+X^2+X X^2 X^2 X^2+X X^3+X X^3 X^3+X^2+X X^3 X^3+X X^3+X^2 X^3 X^3+X^2+X X^3+X X^3+X^2 X^3+X X^2 X^2+X X^3 X^3+X^2  X X^3+X^2+X  X  0  0 X^2+X  X X^2  X X^3 X^3+X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X X^3+X^2+X X^3 X^2  X X^2+X  0  0 X^2+X  X X^2  0 X^2+X X^3+X^2+X X^3 X^3+X^2 X^3+X  X X^2 X^2  X X^2+X  0 X^3 X^3+X^2+X X^3+X X^3+X^2  X  0 X^3+X^2+X X^2  X  0 X^3+X X^3+X X^3+X^2 X^3+X^2+X X^2+X  X X^3 X^3+X^2+X X^3+X^2  X X^2+X X^3  X  X X^3+X^2 X^3+X^2+X  X  X X^3+X  X  0  0 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+118x^93+194x^94+234x^95+92x^96+118x^97+119x^98+70x^99+17x^100+28x^101+8x^102+8x^103+9x^104+2x^106+1x^108+4x^110+1x^130

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 0.703 seconds.