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

generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+120x^81+144x^82+204x^83+122x^84+216x^85+88x^86+80x^87+18x^88+16x^89+8x^90+4x^91+2x^100+1x^128

The gray image is a linear code over GF(2) with n=672, k=10 and d=324.
This code was found by Heurico 1.16 in 2.17 seconds.