The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+311x^46+1510x^47+3865x^48+6062x^49+10734x^50+12926x^51+19821x^52+19566x^53+20527x^54+14292x^55+10792x^56+5456x^57+3198x^58+1160x^59+553x^60+176x^61+72x^62+30x^63+8x^64+2x^65+6x^66+2x^67+2x^69

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 108 seconds.