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

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+144x^70+130x^72+268x^74+216x^76+160x^78+35x^80+60x^82+8x^86+1x^88+1x^136

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 88.2 seconds.