The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+10x^70+8x^71+11x^72+2x^74

The gray image is a linear code over GF(2) with n=276, k=5 and d=140.
This code was found by Heurico 1.16 in 0.141 seconds.