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

generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+61x^76+122x^78+185x^80+256x^81+818x^82+256x^83+226x^84+46x^86+21x^88+38x^90+17x^92+1x^152

The gray image is a linear code over GF(2) with n=656, k=11 and d=304.
This code was found by Heurico 1.16 in 0.765 seconds.