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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+38x^76+112x^77+217x^78+300x^79+226x^80+88x^81+20x^82+12x^83+6x^84+3x^86+1x^152

The gray image is a linear code over GF(2) with n=632, k=10 and d=304.
This code was found by Heurico 1.16 in 0.703 seconds.