The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X^2+X  1 X^3+X^2  1  1 X^3+X  1 X^2  X  1  1  1  1  0 X^2+X  1  1  1  1  1  1 X^3+X^2 X^3+X  1  1  1  1 X^3  1  1 X^3+X^2+X  1  1  1 X^2  X  1  X  1  1  1  1  1  0 X^3+X^2+X  0  X  0 X^3  1  1  1  1  1  1 X^3+X^2+X  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+1 X^3  1 X^2+X+1 X^3+X^2+X  1 X^2  1 X^3+X^2+1  X  1 X+1  1  1 X^3+X^2+X+1 X^3+X^2 X^3+X  1  1  1 X^3+X+1  1  0 X^2+X X^2+X+1 X^3+X^2+1  1  1 X^3+X^2 X^3+X  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X X^3+1  1  1 X^3+X^2+X+1 X^2+X X^2+1 X^3+1 X^3+X+1 X^3+X+1 X^3+X+1  1  1  X  1  1  1 X^3+X^2+X  0 X^3+X^2+X X^3+X X^3+X^2+X+1 X^2  1 X^3+X  0
 0  0 X^2  0 X^3  0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^3 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^2 X^3 X^3 X^3 X^3 X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3 X^2 X^3 X^3+X^2 X^3  0  0 X^3+X^2 X^3 X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^2  0  0
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  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+122x^65+264x^66+258x^67+284x^68+276x^69+242x^70+244x^71+168x^72+114x^73+58x^74+10x^75+2x^76+2x^86+1x^88+2x^90

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 0.36 seconds.