The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1 2X  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  1  X  1  1 2X+2 2X  1  X  X  1  X  X  1  0  1  1  1 2X  1  1
 0  X  0 X+2 2X+2 3X+2  2  X 2X 3X+2  0 3X+2 2X+2 3X 2X+2  X  0 3X+2 3X 3X+2  0  X 3X 2X+2 3X X+2 2X 3X+2 2X+2  0 3X+2  X X+2 3X  X 3X 3X  2 2X+2 3X+2 2X+2 2X  X  X  2 3X 3X+2 3X+2 3X  X 3X  X 3X+2 X+2 2X+2  X  0 2X
 0  0  2  0 2X+2  0  0 2X  0 2X+2 2X+2 2X+2 2X+2  2 2X 2X+2  0  2 2X  2  0  0 2X  2  2  2  2 2X 2X+2 2X  0  2 2X  0 2X+2  2  0 2X 2X+2 2X  0 2X+2  0 2X+2 2X+2 2X+2  0  2 2X 2X+2  2 2X 2X+2  0 2X  2 2X 2X
 0  0  0  2  0  0 2X 2X+2 2X+2 2X+2 2X+2 2X  2  0 2X+2 2X+2  0 2X+2  0 2X  2  2  2  2 2X  2 2X 2X+2 2X+2  2  2 2X+2  2 2X  2  0 2X+2  2 2X  0 2X 2X+2  2  0 2X+2 2X+2 2X  0  0 2X  2  0 2X+2  0 2X 2X+2 2X  0
 0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0 2X 2X  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+66x^52+130x^53+196x^54+350x^55+472x^56+562x^57+617x^58+556x^59+454x^60+328x^61+161x^62+96x^63+50x^64+10x^65+14x^66+4x^67+10x^68+10x^69+1x^70+2x^71+3x^72+2x^74+1x^90

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 0.516 seconds.