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

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+257x^90+32x^91+321x^92+144x^93+654x^94+320x^95+744x^96+352x^97+558x^98+160x^99+249x^100+16x^101+188x^102+54x^104+33x^106+5x^108+6x^110+1x^112+1x^164

The gray image is a linear code over GF(2) with n=768, k=12 and d=360.
This code was found by Heurico 1.16 in 15.5 seconds.