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

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+154x^65+99x^66+308x^67+302x^68+450x^69+290x^70+224x^71+37x^72+54x^73+26x^74+76x^75+12x^76+14x^77+1x^122

The gray image is a linear code over GF(2) with n=552, k=11 and d=260.
This code was found by Heurico 1.16 in 0.391 seconds.