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  X  X  1  1  1  1  X  X  1  1  1  1  X  X  X  X  1  1  1  1 X^2  X  X  0 X^2 X^3  X  X  1  X  X X^2  1  1  1 X^2  0 X^2 X^3  X  X  X  X X^3 X^2 X^2  0  X  X  1 X^2 X^2 X^2 X^3  1  0 X^3
 0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3 X^2 X^2 X^2 X^3+X^2 X^2  0 X^3  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^2  0 X^3 X^3+X^2 X^2 X^3  0 X^3 X^3  0 X^3  0  0 X^3+X^2 X^2  0 X^3 X^2 X^2

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+58x^82+2x^84+2x^86+1x^88

The gray image is a linear code over GF(2) with n=648, k=6 and d=328.
This code was found by Heurico 1.16 in 0.407 seconds.