The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+494x^52+1776x^53+4026x^54+6992x^55+11114x^56+14532x^57+17027x^58+18544x^59+18104x^60+15096x^61+10584x^62+6556x^63+3616x^64+1540x^65+719x^66+216x^67+76x^68+16x^69+24x^70+12x^71+3x^72+4x^74

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 122 seconds.