The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X  1  1 X^3+X^2  1 X^3  1  1 X^2  1  1 X^2+X  1  1  1 X^3+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^3+X^2+X  X X^3+X^2  0 X^2+X X^3+X^2 X^3+X  0 X^3 X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2+X X^3+X^2+X  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X+1 X^3+X^2  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X X^3+X^2+X+1  1 X^3+1 X^3+X^2  1 X^3  1 X+1 X^2+X  1 X^3+X^2+X+1 X^2+1  1 X^2 X^3+X X^3+1  1 X^3+X^2+X  0  X X^3+X^2  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3+X+1 X^2+X+1 X+1
 0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0  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+288x^79+54x^80+160x^81+72x^82+896x^83+72x^84+160x^85+54x^86+288x^87+2x^102+1x^128

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 0.453 seconds.