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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+166x^75+102x^76+186x^77+293x^78+588x^79+283x^80+196x^81+62x^82+110x^83+22x^84+34x^85+4x^86+1x^150

The gray image is a linear code over GF(2) with n=632, k=11 and d=300.
This code was found by Heurico 1.16 in 0.594 seconds.