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

generates a code of length 95 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+62x^82+142x^83+198x^84+302x^85+344x^86+408x^87+570x^88+620x^89+750x^90+922x^91+1061x^92+1148x^93+1131x^94+1268x^95+1223x^96+1114x^97+987x^98+820x^99+781x^100+596x^101+473x^102+370x^103+263x^104+246x^105+165x^106+132x^107+104x^108+58x^109+48x^110+26x^111+19x^112+12x^113+7x^114+8x^115+4x^116+1x^130

The gray image is a linear code over GF(2) with n=380, k=14 and d=164.
This code was found by Heurico 1.16 in 34.3 seconds.