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

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+7x^80+100x^81+6x^82+10x^85+2x^90+2x^93

The gray image is a linear code over GF(2) with n=648, k=7 and d=320.
This code was found by Heurico 1.16 in 0.547 seconds.