The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+508x^56+1804x^57+4478x^58+8260x^59+13828x^60+20956x^61+27248x^62+35388x^63+36344x^64+35668x^65+28538x^66+21428x^67+13396x^68+7844x^69+3850x^70+1508x^71+723x^72+224x^73+72x^74+40x^75+22x^76+6x^78+5x^80+2x^84+3x^88

The gray image is a code over GF(2) with n=512, k=18 and d=224.
This code was found by Heurico 1.16 in 780 seconds.