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

generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+100x^82+128x^83+155x^84+52x^86+64x^87+8x^90+3x^96+1x^116

The gray image is a linear code over GF(2) with n=672, k=9 and d=328.
This code was found by Heurico 1.16 in 0.64 seconds.