The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+930x^52+2170x^53+3596x^54+5462x^55+7130x^56+8844x^57+9171x^58+9010x^59+7563x^60+5380x^61+3360x^62+1696x^63+743x^64+296x^65+112x^66+22x^67+25x^68+14x^69+8x^70+2x^71+1x^74

The gray image is a code over GF(2) with n=464, k=16 and d=208.
This code was found by Heurico 1.16 in 93.2 seconds.