The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+74x^85+331x^86+630x^87+930x^88+1072x^89+1717x^90+1646x^91+2112x^92+1986x^93+2366x^94+2360x^95+2534x^96+2338x^97+2607x^98+2026x^99+2076x^100+1548x^101+1395x^102+912x^103+822x^104+440x^105+295x^106+204x^107+146x^108+70x^109+44x^110+26x^111+17x^112+22x^113+13x^114+4x^115+2x^116+2x^117

The gray image is a linear code over GF(2) with n=384, k=15 and d=170.
This code was found by Heurico 1.16 in 68.9 seconds.