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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+130x^75+24x^76+16x^77+23x^78+8x^79+7x^80+8x^82+36x^83+2x^91+1x^94

The gray image is a linear code over GF(2) with n=308, k=8 and d=150.
This code was found by Heurico 1.16 in 1.06 seconds.