The generator matrix

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

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+284x^46+1516x^47+3164x^48+7208x^49+9660x^50+15078x^51+18103x^52+20606x^53+18768x^54+15736x^55+9390x^56+6540x^57+2816x^58+1478x^59+456x^60+166x^61+70x^62+16x^63+5x^64+8x^65+1x^68+2x^70

The gray image is a code over GF(2) with n=424, k=17 and d=184.
This code was found by Heurico 1.16 in 112 seconds.