The generator matrix

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

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+118x^64+630x^65+626x^66+690x^67+532x^68+510x^69+274x^70+270x^71+147x^72+108x^73+58x^74+72x^75+33x^76+24x^77+1x^78+1x^84+1x^86

The gray image is a linear code over GF(2) with n=544, k=12 and d=256.
This code was found by Heurico 1.16 in 2.38 seconds.