The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+31x^86+72x^87+204x^88+330x^89+448x^90+492x^91+470x^92+628x^93+669x^94+602x^95+619x^96+598x^97+526x^98+584x^99+513x^100+366x^101+360x^102+234x^103+137x^104+106x^105+43x^106+40x^107+22x^108+12x^109+23x^110+18x^111+11x^112+6x^113+10x^114+4x^115+6x^116+2x^117+2x^119+1x^124+1x^126+1x^130

The gray image is a linear code over GF(2) with n=384, k=13 and d=172.
This code was found by Heurico 1.16 in 6.97 seconds.