The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1 X^3+X  1  0  1  1  1  1  1 X^3 X^3+X^2+X  1  1  1  1  1 X^3  X X^2  1  1 X^2+X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1 X^2  1  1  X
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1  0  1 X^2+1  1 X^3+X^2+X X^3+X+1 X^2 X^3+X^2+1 X^2+X  1  1 X^3+1 X^3+X^2 X^3+X X^2+X X^3+X+1  1  1  1 X^3  1  1  0  X X^2 X^3+X X^3 X^2 X^3+X^2 X^3+X  X X^2 X^2 X^3+X X^3+X^2+X X^2+X X^2+X X^3+X^2 X^3+X^2+1 X^2+X X^2  1 X^2  0 X^3+X
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^2  0  0 X^3 X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0 X^3  0  0 X^3  0 X^2 X^3 X^3 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2  0
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0 X^3  0  0  0
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3

generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+121x^66+292x^67+361x^68+560x^69+548x^70+572x^71+418x^72+448x^73+339x^74+236x^75+97x^76+48x^77+8x^78+20x^79+11x^80+6x^82+6x^84+2x^86+2x^100

The gray image is a linear code over GF(2) with n=568, k=12 and d=264.
This code was found by Heurico 1.16 in 0.563 seconds.