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

generates a code of length 68 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+217x^64+112x^65+261x^66+84x^67+700x^68+112x^69+274x^70+40x^71+200x^72+32x^73+9x^74+4x^75+1x^92+1x^100

The gray image is a linear code over GF(2) with n=544, k=11 and d=256.
This code was found by Heurico 1.16 in 0.235 seconds.