The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+158x^54+1056x^55+2254x^56+3712x^57+5906x^58+6458x^59+9036x^60+8638x^61+9002x^62+6648x^63+5933x^64+3246x^65+1852x^66+1026x^67+346x^68+130x^69+52x^70+60x^71+12x^72+2x^73+6x^74+2x^76

The gray image is a code over GF(2) with n=488, k=16 and d=216.
This code was found by Heurico 1.16 in 34.5 seconds.