The generator matrix

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

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+386x^81+265x^82+442x^83+89x^84+308x^85+181x^86+244x^87+21x^88+62x^89+16x^90+22x^91+1x^92+4x^95+4x^97+1x^106+1x^126

The gray image is a linear code over GF(2) with n=672, k=11 and d=324.
This code was found by Heurico 1.16 in 3.72 seconds.