The generator matrix

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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+134x^70+58x^72+96x^73+84x^74+320x^75+40x^76+96x^77+104x^78+28x^80+60x^82+2x^86+1x^144

The gray image is a linear code over GF(2) with n=300, k=10 and d=140.
This code was found by Heurico 1.16 in 13.8 seconds.