The generator matrix

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

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+239x^52+1048x^53+1926x^54+2700x^55+3824x^56+4686x^57+4689x^58+4282x^59+3615x^60+2584x^61+1633x^62+840x^63+345x^64+214x^65+64x^66+18x^67+40x^68+12x^69+7x^70+1x^74

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 9.36 seconds.