The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+251x^46+1544x^47+3398x^48+6726x^49+10155x^50+14874x^51+17968x^52+20724x^53+18401x^54+15800x^55+10077x^56+6088x^57+3034x^58+1334x^59+378x^60+220x^61+58x^62+14x^63+18x^64+2x^65+5x^66+2x^71

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 110 seconds.