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

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+104x^67+129x^68+96x^69+108x^70+20x^71+12x^72+30x^73+2x^74+4x^75+1x^76+1x^78+1x^80+2x^81+1x^86

The gray image is a linear code over GF(2) with n=552, k=9 and d=268.
This code was found by Heurico 1.16 in 0.547 seconds.