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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+28x^90+46x^91+51x^92+72x^93+162x^94+396x^95+554x^96+402x^97+164x^98+62x^99+25x^100+36x^101+21x^102+8x^103+9x^104+2x^105+8x^106+1x^182

The gray image is a linear code over GF(2) with n=768, k=11 and d=360.
This code was found by Heurico 1.16 in 1.27 seconds.