The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+112x^75+161x^76+156x^77+141x^78+94x^79+95x^80+64x^81+51x^82+32x^83+27x^84+12x^85+22x^86+10x^87+8x^88+20x^89+8x^91+2x^92+4x^93+1x^94+2x^96+1x^98

The gray image is a linear code over GF(2) with n=316, k=10 and d=150.
This code was found by Heurico 1.11 in 0.234 seconds.