The generator matrix

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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+204x^92+678x^93+774x^94+610x^95+404x^96+342x^97+255x^98+202x^99+164x^100+156x^101+121x^102+100x^103+40x^104+24x^105+17x^106+1x^108+1x^112+1x^116+1x^126

The gray image is a linear code over GF(2) with n=768, k=12 and d=368.
This code was found by Heurico 1.16 in 2.23 seconds.