The generator matrix

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

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+194x^65+308x^66+464x^67+338x^68+390x^69+348x^70+398x^71+277x^72+334x^73+232x^74+222x^75+132x^76+182x^77+73x^78+54x^79+48x^80+48x^81+30x^82+10x^83+4x^84+4x^85+1x^86+4x^87

The gray image is a linear code over GF(2) with n=284, k=12 and d=130.
This code was found by Heurico 1.16 in 0.77 seconds.