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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+56x^65+44x^66+40x^67+90x^68+98x^69+136x^70+130x^71+128x^72+104x^73+64x^74+36x^75+28x^76+26x^77+8x^78+18x^79+6x^80+4x^81+4x^82+2x^84+1x^128

The gray image is a linear code over GF(2) with n=284, k=10 and d=130.
This code was found by Heurico 1.16 in 1.17 seconds.