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

generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+568x^79+212x^80+800x^81+186x^82+756x^83+176x^84+680x^85+164x^86+420x^87+20x^88+48x^89+2x^90+28x^91+2x^92+8x^93+20x^95+3x^96+2x^116

The gray image is a linear code over GF(2) with n=664, k=12 and d=316.
This code was found by Heurico 1.16 in 47.8 seconds.