The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+110x^55+954x^56+2042x^57+4212x^58+5436x^59+7170x^60+8364x^61+9427x^62+8142x^63+7578x^64+5192x^65+3443x^66+1828x^67+1088x^68+308x^69+126x^70+48x^71+41x^72+14x^73+7x^74+4x^75+1x^78

The gray image is a code over GF(2) with n=496, k=16 and d=220.
This code was found by Heurico 1.16 in 32.2 seconds.