The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^53+695x^54+1910x^55+4134x^56+8004x^57+13584x^58+19916x^59+29568x^60+34628x^61+36844x^62+34664x^63+29640x^64+21244x^65+13298x^66+7210x^67+3883x^68+1608x^69+775x^70+232x^71+161x^72+48x^73+18x^74+2x^75+5x^76+2x^78+2x^79

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 566 seconds.