The generator matrix

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

generates a code of length 84 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+182x^80+640x^81+710x^82+624x^83+529x^84+384x^85+266x^86+256x^87+134x^88+96x^89+81x^90+88x^91+49x^92+16x^93+21x^94+8x^95+9x^96+1x^98+1x^102

The gray image is a linear code over GF(2) with n=672, k=12 and d=320.
This code was found by Heurico 1.16 in 9.77 seconds.