The generator matrix

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

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+737x^80+874x^82+981x^84+796x^86+635x^88+26x^90+27x^92+16x^96+3x^112

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 64.9 seconds.