The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+54x^71+129x^72+202x^73+426x^74+512x^75+595x^76+792x^77+994x^78+1078x^79+1305x^80+1452x^81+1394x^82+1468x^83+1283x^84+1224x^85+987x^86+746x^87+601x^88+332x^89+216x^90+200x^91+144x^92+80x^93+55x^94+26x^95+28x^96+12x^97+20x^98+12x^99+9x^100+3x^102+2x^105+1x^108+1x^110

The gray image is a linear code over GF(2) with n=328, k=14 and d=142.
This code was found by Heurico 1.16 in 20.9 seconds.