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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+47x^70+24x^71+81x^72+16x^73+14x^74+20x^75+14x^76+35x^78+2x^79+2x^103

The gray image is a linear code over GF(2) with n=292, k=8 and d=140.
This code was found by Heurico 1.16 in 0.244 seconds.