The generator matrix

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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+200x^91+406x^92+632x^93+176x^94+448x^95+370x^96+448x^97+176x^98+632x^99+402x^100+200x^101+2x^104+1x^120+1x^128+1x^136

The gray image is a linear code over GF(2) with n=768, k=12 and d=364.
This code was found by Heurico 1.16 in 1.14 seconds.