The generator matrix

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

generates a code of length 68 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+280x^65+407x^66+380x^67+187x^68+264x^69+223x^70+148x^71+35x^72+52x^73+41x^74+16x^75+4x^77+8x^81+1x^92+1x^94

The gray image is a linear code over GF(2) with n=544, k=11 and d=260.
This code was found by Heurico 1.16 in 0.406 seconds.