The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+336x^47+856x^48+1564x^49+2123x^50+2338x^51+2491x^52+2182x^53+1824x^54+1316x^55+724x^56+344x^57+123x^58+86x^59+39x^60+18x^61+6x^62+4x^63+1x^64+4x^65+4x^66

The gray image is a code over GF(2) with n=416, k=14 and d=188.
This code was found by Heurico 1.16 in 2.02 seconds.