The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+92x^52+918x^53+2246x^54+3936x^55+5280x^56+7488x^57+8096x^58+9220x^59+8771x^60+7680x^61+5130x^62+3434x^63+1666x^64+936x^65+404x^66+152x^67+45x^68+18x^69+12x^70+10x^71+1x^72

The gray image is a code over GF(2) with n=472, k=16 and d=208.
This code was found by Heurico 1.16 in 32.3 seconds.