The generator matrix

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

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+572x^92+408x^93+625x^94+376x^95+543x^96+272x^97+446x^98+224x^99+302x^100+120x^101+125x^102+8x^103+31x^104+20x^106+16x^108+4x^112+2x^120+1x^128

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 133 seconds.