The generator matrix

 1  0  0  1  1  1 X+2 X+2  1 X+2 X^2+X+2  1  1  1  1  1  1  0  1  X  X  0  1  1  X X^2  1  1  1 X^2  2  1 X^2  1  1  1 X^2+X+2 X+2  1  0  1 X^2+X  1  1 X^2+2  2  X  1  2  1  1  X  X X^2+X+2 X^2+2  1  1  1
 0  1  0  0 X^2+1 X+1  1  1 X^2+X X^2  1 X^2+1 X+3 X^2+X X^2+2  3 X^2+X+3  1 X+2  1  0  1 X^2  1  1  1  1  X X+3  2  1 X^2+X+2  1 X^2+X+2 X+3 X^2+2  1  1 X^2  1  0  1 X^2 X^2+1  1  1  1  3  1 X+2 X^2+X X^2+2  1 X^2+2 X+2 X^2 X^2+1 X+2
 0  0  1  1  1  0  1  X  2  1 X^2+X+1 X^2+X+3 X^2+X+2  3 X^2+X+2 X^2+X X^2+1 X+1 X^2+X+3  X  1 X+2 X+3 X^2+X+3  3  3 X^2 X+2  3  1 X^2+X X^2+X+1 X^2+X+3 X^2+1 X^2+X  X X^2+2  X  0  1 X^2+2 X^2 X^2+X+1 X+1  2 X^2+2  0 X+2  2  1  0  1 X+3  1  1 X^2+X  X X+3
 0  0  0  X X+2  2 X+2 X^2  0  X X^2+X X^2+X+2  2 X^2+X+2 X^2  0 X^2+X X+2  X X^2+X+2 X^2+2  X X^2+X+2  2  0 X^2+2  X  2 X^2 X^2+X X^2 X^2+2  0  2 X+2  X  2  X  X X^2+X+2 X^2 X^2+X  0 X^2+2  X X^2+X X^2+X X^2 X^2+2  X X^2+X  2  0 X^2+X+2 X^2+X X^2+X X^2  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+260x^52+998x^53+1787x^54+3120x^55+3789x^56+4452x^57+4619x^58+4262x^59+3534x^60+2834x^61+1484x^62+876x^63+450x^64+192x^65+67x^66+30x^67+5x^68+4x^69+3x^70+1x^76

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 8.39 seconds.