The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+66x^53+558x^54+1878x^55+4503x^56+7892x^57+13597x^58+20102x^59+29068x^60+34314x^61+37568x^62+34872x^63+29588x^64+20524x^65+13271x^66+7566x^67+4120x^68+1454x^69+724x^70+294x^71+102x^72+48x^73+10x^74+8x^75+6x^76+6x^77+4x^80

The gray image is a code over GF(2) with n=496, k=18 and d=212.
This code was found by Heurico 1.16 in 520 seconds.