The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+172x^47+859x^48+1680x^49+3014x^50+3816x^51+4749x^52+4594x^53+4764x^54+3724x^55+2653x^56+1384x^57+783x^58+308x^59+173x^60+54x^61+18x^62+12x^63+3x^64+5x^66+2x^68

The gray image is a code over GF(2) with n=424, k=15 and d=188.
This code was found by Heurico 1.16 in 7.97 seconds.