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  0  X  0  X X^2  X X^2  1  1  X  0  X  1  0  X  1  1 X^2 X^2  X  0  1  1  1  X  0  1  X  1  0  X  1 X^2  X  1  X  1  1 X^2  1  X  1  0  X  X  0 X^2 X^2
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  0 X^2+X  X  X X^2+X X^2+X  0  X  0 X^2+X X^2 X^2  0  0  X  0 X^2  X X^2+X  0  X X^2+X X^2  X  0  X X^2  X X^2  0 X^2+X X^2  X  X  X X^2+X  X  X  X  X X^2  X  X X^2+X  0 X^2  X  X  X X^2 X^2  X  X X^2+X X^2 X^2  0 X^2 X^2+X  X X^2  X  X  X  X  X  X  0  X  X  X X^2+X X^2  X  X  X  X X^2+X  0  X  X X^2
 0  0  X  0  X  X X^2+X  0  0  0  X X^2  X X^2+X X^2 X^2+X  X X^2  0 X^2  X X^2 X^2+X X^2+X  X  X  0  0  0 X^2  0  0 X^2+X  0 X^2  X  X X^2  X X^2+X  X X^2+X X^2  0 X^2  X  0 X^2  0  0 X^2+X X^2  0  X  X X^2+X  X  X X^2+X  0 X^2+X X^2 X^2  0 X^2+X  0  X X^2 X^2  X X^2  X X^2+X X^2+X  X  0 X^2 X^2+X X^2+X  X  X X^2  X  X  X  X  0  0 X^2 X^2+X  0  X  0  X X^2
 0  0  0  X  X  0 X^2+X  X  0  X  0  X X^2+X X^2+X X^2 X^2  X  X X^2 X^2 X^2  X  X X^2+X X^2 X^2  0 X^2  X  X X^2+X X^2+X  X X^2 X^2 X^2+X  0 X^2 X^2 X^2 X^2  X  X  X X^2 X^2+X X^2+X X^2 X^2 X^2  0 X^2+X X^2+X  X X^2  0  X X^2  X X^2+X  X X^2+X  X  0  0  X  0  X X^2+X X^2  X X^2  X  X  X  0  0  0 X^2+X  X X^2 X^2  0 X^2  X  0  0 X^2+X X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 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 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  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  0 X^2  0  0  0  0  0  0  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 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+146x^82+8x^83+393x^84+72x^85+637x^86+128x^87+894x^88+300x^89+1123x^90+484x^91+1484x^92+592x^93+1603x^94+824x^95+1540x^96+752x^97+1458x^98+456x^99+1094x^100+288x^101+683x^102+136x^103+493x^104+36x^105+392x^106+12x^107+202x^108+8x^109+81x^110+31x^112+16x^114+9x^116+4x^118+1x^120+1x^122+2x^124

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 36.3 seconds.