The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+296x^52+1090x^53+1781x^54+2972x^55+3299x^56+5050x^57+4113x^58+5192x^59+3044x^60+2858x^61+1590x^62+784x^63+348x^64+182x^65+97x^66+40x^67+18x^68+4x^69+3x^70+4x^71+2x^72

The gray image is a code over GF(2) with n=464, k=15 and d=208.
This code was found by Heurico 1.16 in 8.55 seconds.