The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^54+1012x^55+2206x^56+3724x^57+5412x^58+7244x^59+8544x^60+9240x^61+8782x^62+7416x^63+5176x^64+3444x^65+1734x^66+908x^67+366x^68+128x^69+50x^70+28x^71+35x^72+8x^73+2x^74

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 30.6 seconds.