The generator matrix

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

generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+102x^67+734x^68+544x^69+714x^70+462x^71+581x^72+240x^73+275x^74+98x^75+146x^76+56x^77+81x^78+26x^79+21x^80+8x^81+1x^82+4x^84+1x^86+1x^88

The gray image is a linear code over GF(2) with n=568, k=12 and d=268.
This code was found by Heurico 1.16 in 0.281 seconds.