The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+68x^83+153x^84+200x^85+321x^86+298x^87+407x^88+548x^89+601x^90+744x^91+923x^92+1002x^93+1194x^94+1252x^95+1211x^96+1306x^97+1035x^98+1040x^99+878x^100+704x^101+653x^102+458x^103+342x^104+220x^105+186x^106+176x^107+137x^108+94x^109+84x^110+56x^111+38x^112+22x^113+17x^114+4x^115+5x^116+3x^118+1x^120+1x^122+1x^134

The gray image is a linear code over GF(2) with n=384, k=14 and d=166.
This code was found by Heurico 1.16 in 36.3 seconds.