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

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+69x^74+88x^75+94x^76+116x^77+49x^78+20x^79+10x^80+16x^81+12x^82+8x^83+14x^84+4x^86+4x^87+1x^88+4x^89+1x^90+1x^94

The gray image is a linear code over GF(2) with n=308, k=9 and d=148.
This code was found by Heurico 1.11 in 0.125 seconds.