The generator matrix

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

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+52x^64+372x^65+285x^66+254x^67+239x^68+302x^69+168x^70+164x^71+119x^72+36x^73+25x^74+20x^75+4x^76+2x^77+2x^82+1x^84+2x^91

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 0.344 seconds.