The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+66x^74+96x^75+63x^76+108x^77+72x^78+28x^79+42x^80+12x^81+2x^82+4x^83+2x^84+8x^85+4x^90+3x^92+1x^96

The gray image is a linear code over GF(2) with n=308, k=9 and d=148.
This code was found by Heurico 1.16 in 0.158 seconds.