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  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^2  1  1 X^2
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X X^3+X^2  0 X^2+X X^3+X^2  X  0 X^2+X X^3+X X^3+X^2 X^2+X  0  X X^3+X^2  0 X^2+X X^3+X X^3+X^2  0 X^2+X X^3+X^2 X^3+X X^3+X  0 X^3+X^2 X^2+X X^3 X^3+X^2+X X^2  X X^3+X  0 X^3+X^2 X^2+X X^3 X^3+X^2+X X^2  X  0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^3+X X^2 X^3+X X^3+X  0 X^3 X^3+X X^3+X^2 X^2 X^2+X X^3+X^2+X  X X^3 X^3 X^3+X^2+X X^3+X^2+X X^2 X^2 X^3+X^2+X X^3+X^2+X X^3 X^3 X^2 X^2 X^3+X  X X^3+X  X  X  0  0 X^3 X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3 X^2+X X^3 X^3+X^2 X^2+X X^3 X^3+X^2
 0  0 X^3  0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  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  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 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+195x^92+272x^94+1147x^96+224x^98+188x^100+16x^102+4x^104+1x^188

The gray image is a linear code over GF(2) with n=768, k=11 and d=368.
This code was found by Heurico 1.16 in 1.22 seconds.