The generator matrix

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

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+126x^65+79x^66+282x^67+76x^68+284x^69+142x^70+222x^71+46x^72+262x^73+96x^74+222x^75+32x^76+86x^77+34x^78+30x^79+4x^81+1x^82+8x^83+3x^84+6x^85+4x^87+1x^96+1x^100

The gray image is a linear code over GF(2) with n=284, k=11 and d=130.
This code was found by Heurico 1.16 in 2.05 seconds.