The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+496x^56+1986x^57+4260x^58+8802x^59+12479x^60+21390x^61+28040x^62+35056x^63+36277x^64+36432x^65+27369x^66+22096x^67+13062x^68+7920x^69+3761x^70+1676x^71+614x^72+258x^73+82x^74+46x^75+15x^76+10x^77+7x^78+4x^79+4x^81+1x^90

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 555 seconds.