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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+45x^80+12x^81+65x^82+26x^83+40x^84+20x^85+28x^86+4x^87+10x^88+3x^98+2x^99

The gray image is a linear code over GF(2) with n=332, k=8 and d=160.
This code was found by Heurico 1.16 in 0.397 seconds.