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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+117x^64+20x^65+212x^66+64x^67+255x^68+84x^69+244x^70+160x^71+222x^72+124x^73+202x^74+32x^75+112x^76+28x^77+76x^78+51x^80+24x^82+9x^84+8x^86+2x^90+1x^112

The gray image is a linear code over GF(2) with n=284, k=11 and d=128.
This code was found by Heurico 1.16 in 0.484 seconds.