The generator matrix

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

generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+360x^68+332x^69+357x^70+176x^71+230x^72+200x^73+248x^74+48x^75+56x^76+12x^77+17x^78+8x^80+1x^86+1x^94+1x^96

The gray image is a linear code over GF(2) with n=568, k=11 and d=272.
This code was found by Heurico 1.16 in 1.16 seconds.