The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+420x^90+801x^92+858x^94+626x^96+458x^98+316x^100+242x^102+144x^104+90x^106+83x^108+36x^110+13x^112+8x^114

The gray image is a linear code over GF(2) with n=384, k=12 and d=180.
This code was found by Heurico 1.11 in 2.16 seconds.