The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+60x^56+658x^57+1829x^58+4478x^59+8065x^60+14184x^61+21041x^62+27626x^63+33232x^64+37714x^65+35405x^66+28984x^67+21128x^68+13456x^69+7238x^70+4026x^71+1745x^72+812x^73+241x^74+126x^75+54x^76+20x^77+5x^78+8x^79+2x^80+4x^81+1x^82+1x^84

The gray image is a code over GF(2) with n=520, k=18 and d=224.
This code was found by Heurico 1.16 in 555 seconds.