The generator matrix

 1  0  0  0  1  1  1  1 3X  1 3X 3X+2  1  1  2  1  1  2 3X+2  1  0  1  1  1 X+2  1  1  X  1  X  X 3X  1  1  1  1 2X  1  X  2 2X+2  1 X+2 2X+2  1  1  1  2 3X  1  2 3X  1  1  1  1 2X  1 X+2
 0  1  0  0  X 2X+3 X+2 X+1  1 3X 2X+2  1  3 3X+3  1  0  2  1  1 2X+1 3X X+2 X+2  3  0 2X+1  1  X 2X  1  1  1 3X+3 X+3  2 2X  0 3X+3  1  1  2 3X+2  1  0 2X+3 2X+3 2X+2 3X+2 3X 3X+2  1  1 2X+1 3X+3 2X+2  X  1 3X+3 3X+2
 0  0  1  0  0 2X 3X+1 2X+1 2X+3  3  1  0 X+1  2 X+3 X+2 3X+2  1 X+3  2  X 2X+1 2X+3  1  1  1 3X  1  1 3X X+2 2X+3  X X+1  3 X+2  X 2X 2X+2 3X+2  1  2 3X+1  1 2X+1  2 3X+3 2X  1 2X+1 2X+1 2X+2  X 2X+1 3X+1 3X  2 2X+1  1
 0  0  0  1  1 3X+1 X+1 2X+1 2X 2X  1 2X+1 2X+2  2 2X+1 2X 2X+3 3X+2 3X+1  X  1 X+3 X+2  3 X+1 2X+2 2X+3 X+2 X+2 3X+1 3X+2 X+3 2X X+3 2X  X  1 2X+3 3X+2 3X+2 X+2 3X+3  3 3X+3 3X+3  2  3  1 2X+2  3 2X+3  0 X+1 2X  X 2X+1  1 X+2 X+1
 0  0  0  0 2X 2X 2X 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0  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+459x^52+1772x^53+4267x^54+6978x^55+10892x^56+14408x^57+17291x^58+18154x^59+18281x^60+14898x^61+11130x^62+6418x^63+3559x^64+1636x^65+547x^66+206x^67+110x^68+38x^69+13x^70+4x^71+6x^72+4x^76

The gray image is a code over GF(2) with n=472, k=17 and d=208.
This code was found by Heurico 1.16 in 125 seconds.