The generator matrix

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

generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+100x^65+756x^66+1118x^67+1630x^68+1732x^69+2314x^70+1836x^71+2190x^72+1336x^73+1439x^74+764x^75+506x^76+274x^77+160x^78+112x^79+69x^80+12x^81+11x^82+10x^83+12x^84+2x^85

The gray image is a linear code over GF(2) with n=568, k=14 and d=260.
This code was found by Heurico 1.16 in 4.38 seconds.