The generator matrix

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

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+112x^75+48x^76+88x^77+50x^78+112x^79+6x^80+48x^81+13x^82+14x^83+6x^84+8x^85+2x^88+2x^99+1x^104+1x^106

The gray image is a linear code over GF(2) with n=312, k=9 and d=150.
This code was found by Heurico 1.16 in 11.5 seconds.