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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+12x^76+88x^77+12x^78+3x^80+8x^81+3x^82+1x^98

The gray image is a linear code over GF(2) with n=308, k=7 and d=152.
This code was found by Heurico 1.16 in 0.219 seconds.