The generator matrix

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

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+33x^52+96x^53+270x^54+292x^55+556x^56+456x^57+715x^58+444x^59+576x^60+272x^61+225x^62+92x^63+47x^64+8x^65+2x^66+4x^67+3x^68+1x^70+2x^74+1x^82

The gray image is a code over GF(2) with n=464, k=12 and d=208.
This code was found by Heurico 1.16 in 0.281 seconds.