The generator matrix

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

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+72x^90+152x^91+253x^92+200x^93+255x^94+210x^95+204x^96+94x^97+108x^98+76x^99+103x^100+56x^101+50x^102+46x^103+52x^104+34x^105+12x^106+12x^107+10x^108+16x^109+23x^110+9x^112

The gray image is a linear code over GF(2) with n=384, k=11 and d=180.
This code was found by Heurico 1.11 in 0.5 seconds.