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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+60x^75+103x^76+86x^77+119x^78+40x^79+35x^80+6x^81+15x^82+8x^83+12x^84+16x^85+4x^87+1x^90+4x^91+1x^96+1x^98

The gray image is a linear code over GF(2) with n=312, k=9 and d=150.
This code was found by Heurico 1.11 in 0.125 seconds.