The generator matrix

 1  0  0  0  1  1  1  X  1  1 X^2+X  1  1  X X^2  1 X^2  1  1  1  0  X  X X^2+X  1  0  1  1  1  0  1 X^2  1 X^2  1  1 X^2  1 X^2+X  X X^2+X  X  1  1  1  1  X  0  1 X^2  1  1  1  1  1  1  1  1 X^2  1  1  1  X  1 X^2  X  X X^2+X  1  0  1  1 X^2+X  0 X^2+X  1  X  1  0  1  1  1  0 X^2+X  X  1  0  1 X^2  0  1  1  1 X^2 X^2  1
 0  1  0  0  X  1 X^2+X+1  1 X+1 X^2  1  X X^2+1  1  0 X^2  1  X X^2+X X^2+1  0  1  1 X^2 X+1  X  1  X  0  1  0  1  1  1 X^2+1  X  1 X^2+X  0  1  X  1 X^2  0 X+1 X^2+X+1  1  X  1  1 X^2+X X+1  1  0 X^2 X^2+1 X^2 X^2+X  1  0 X+1  1  1  X X^2+X  X  0  1 X^2+X+1  1  0  1  0 X^2+X  0  1 X^2 X+1  1  1  1  0  1  1  1 X^2+X+1  1 X^2+X  1 X^2+X  X  0  1  X  1  0
 0  0  1  0  0  0  0 X^2 X^2+1 X^2+1  1  1 X^2+X+1 X^2+X+1  1 X^2+X X^2+X X+1 X^2+X+1  0  X X^2 X^2+X+1  1  X  1 X+1 X^2+X  X X^2+1 X+1  0 X^2+X+1 X^2 X^2  0 X^2+X+1  1 X^2 X^2+X+1  1 X^2+1  1 X^2+X X^2+X+1 X^2+1  X  1 X^2+1 X+1  0 X^2+X  1  0 X^2+X  X  1 X^2+1  X X^2+X+1 X^2+X+1  X  X X^2+X  X  1 X^2+X X^2+X X^2+X+1  1  0 X^2+X  1  1 X^2+X  X  1 X+1 X^2 X^2+X+1 X^2 X^2+X+1 X^2+X X^2+X+1 X^2+1  1  X X^2+X+1  0  1  X X+1 X+1  0 X^2+X  0
 0  0  0  1  1 X^2+X+1 X^2+X X^2+1 X+1  1 X^2  0  X X+1 X^2+X+1 X+1  0  1  X X^2  1 X+1 X^2+X+1 X^2+1 X+1  X  0  1 X^2  0 X^2+X  X X^2+1 X+1  X X^2+X X^2+1 X^2+1  1 X^2+X  1 X^2+X+1  X X^2 X^2+X+1 X^2+1  X X+1  X X^2 X^2+X  0 X^2 X^2+1  0 X+1 X^2+1 X+1  1  1 X^2+1  X X^2+1 X^2+X+1  1 X^2  1 X^2  X X^2 X+1 X^2+X+1  X X^2+1  1  1 X^2+X+1 X^2 X^2+X+1  1  1 X^2+X X^2  1 X^2+X+1 X^2+X+1 X+1 X^2+X X^2 X^2+X X^2 X^2+1 X^2+1  1  X  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 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+92x^85+338x^86+556x^87+1065x^88+1118x^89+1546x^90+1532x^91+2237x^92+1848x^93+2737x^94+2172x^95+2728x^96+2010x^97+2761x^98+1892x^99+2159x^100+1392x^101+1481x^102+934x^103+872x^104+498x^105+317x^106+184x^107+136x^108+68x^109+30x^110+24x^111+10x^112+14x^113+2x^114+8x^116+2x^118+2x^119+2x^122

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 68.4 seconds.