The generator matrix

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

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+166x^65+355x^66+330x^67+465x^68+408x^69+409x^70+334x^71+309x^72+244x^73+288x^74+168x^75+152x^76+166x^77+74x^78+58x^79+84x^80+22x^81+33x^82+22x^83+5x^84+2x^85+1x^86

The gray image is a linear code over GF(2) with n=284, k=12 and d=130.
This code was found by Heurico 1.11 in 0.344 seconds.