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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+42x^82+32x^83+39x^84+6x^86+5x^88+2x^92+1x^108

The gray image is a linear code over GF(2) with n=332, k=7 and d=164.
This code was found by Heurico 1.16 in 0.293 seconds.