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

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+60x^83+155x^84+216x^85+254x^86+318x^87+450x^88+582x^89+678x^90+820x^91+901x^92+916x^93+1132x^94+1208x^95+1114x^96+1214x^97+1168x^98+1022x^99+924x^100+788x^101+574x^102+434x^103+360x^104+278x^105+214x^106+160x^107+165x^108+80x^109+72x^110+52x^111+19x^112+22x^113+4x^114+18x^115+4x^116+4x^119+2x^124+1x^132

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 35 seconds.