The generator matrix

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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+786x^52+2472x^53+3280x^54+5540x^55+7030x^56+9468x^57+8857x^58+9164x^59+7015x^60+5654x^61+3176x^62+1832x^63+731x^64+368x^65+89x^66+52x^67+5x^68+6x^69+6x^70+4x^71

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 31.7 seconds.