The generator matrix

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

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+810x^52+2024x^53+4010x^54+5240x^55+7540x^56+8536x^57+9434x^58+8628x^59+7685x^60+5192x^61+3514x^62+1532x^63+930x^64+272x^65+110x^66+52x^67+9x^68+8x^69+4x^70+4x^71+1x^72

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 53.8 seconds.