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

generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+64x^75+91x^76+256x^77+64x^79+31x^80+2x^84+1x^92+2x^100

The gray image is a linear code over GF(2) with n=616, k=9 and d=300.
This code was found by Heurico 1.16 in 0.984 seconds.