The generator matrix

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

generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+348x^80+336x^81+364x^82+192x^83+265x^84+160x^85+220x^86+64x^87+51x^88+16x^89+20x^90+1x^92+4x^94+4x^96+1x^108+1x^124

The gray image is a linear code over GF(2) with n=664, k=11 and d=320.
This code was found by Heurico 1.16 in 0.484 seconds.