The generator matrix

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

generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+24x^76+18x^77+46x^78+76x^79+35x^80+154x^81+352x^82+660x^83+416x^84+62x^85+92x^86+20x^87+18x^88+14x^89+15x^90+12x^91+16x^92+8x^93+6x^94+2x^96+1x^154

The gray image is a linear code over GF(2) with n=664, k=11 and d=304.
This code was found by Heurico 1.16 in 0.782 seconds.