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

generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+146x^69+85x^70+136x^71+9x^72+60x^73+24x^74+40x^75+4x^76+2x^77+2x^78+1x^80+1x^86+1x^88

The gray image is a linear code over GF(2) with n=568, k=9 and d=276.
This code was found by Heurico 1.16 in 6.41 seconds.