The generator matrix

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

generates a code of length 57 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+439x^50+1854x^51+3915x^52+6652x^53+10154x^54+14366x^55+18626x^56+19238x^57+18209x^58+15038x^59+10166x^60+6504x^61+3609x^62+1394x^63+547x^64+176x^65+104x^66+52x^67+7x^68+4x^69+13x^70+2x^72+2x^73

The gray image is a code over GF(2) with n=456, k=17 and d=200.
This code was found by Heurico 1.16 in 125 seconds.