The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+214x^87+454x^88+622x^89+856x^90+1054x^91+1204x^92+1252x^93+1233x^94+1208x^95+1142x^96+1076x^97+1059x^98+992x^99+894x^100+776x^101+621x^102+528x^103+420x^104+248x^105+211x^106+154x^107+66x^108+50x^109+18x^110+8x^111+11x^112+6x^113+2x^114+2x^117+2x^119

The gray image is a linear code over GF(2) with n=384, k=14 and d=174.
This code was found by Heurico 1.13 in 6.3 seconds.