The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+632x^50+648x^51+751x^52+520x^53+620x^54+232x^55+283x^56+184x^57+128x^58+16x^59+75x^60+4x^62+1x^64+1x^72

The gray image is a code over GF(2) with n=424, k=12 and d=200.
This code was found by Heurico 1.16 in 4.77 seconds.