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

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+16x^68+34x^69+16x^70+382x^71+13x^72+28x^73+16x^74+2x^75+2x^76+2x^105

The gray image is a linear code over GF(2) with n=568, k=9 and d=272.
This code was found by Heurico 1.16 in 0.344 seconds.