The generator matrix

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

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+80x^79+291x^80+312x^81+290x^82+272x^83+221x^84+160x^85+234x^86+108x^87+45x^88+24x^89+3x^90+2x^91+1x^96+2x^99+1x^114+1x^116

The gray image is a linear code over GF(2) with n=664, k=11 and d=316.
This code was found by Heurico 1.16 in 0.687 seconds.