The generator matrix

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

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+220x^65+84x^66+344x^67+81x^68+536x^69+172x^70+352x^71+26x^72+204x^73+16x^74+8x^75+1x^76+1x^80+1x^92+1x^100

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 0.25 seconds.