The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+193x^46+854x^47+1647x^48+2872x^49+3852x^50+4692x^51+4921x^52+4628x^53+3752x^54+2674x^55+1387x^56+784x^57+301x^58+112x^59+56x^60+20x^61+13x^62+4x^63+3x^64+1x^66+1x^68

The gray image is a code over GF(2) with n=416, k=15 and d=184.
This code was found by Heurico 1.16 in 7.34 seconds.