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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+61x^76+116x^77+80x^78+80x^79+77x^80+20x^81+10x^82+12x^83+20x^84+16x^85+4x^86+8x^87+4x^91+1x^92+2x^94

The gray image is a linear code over GF(2) with n=316, k=9 and d=152.
This code was found by Heurico 1.11 in 0.125 seconds.