The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+316x^51+149x^52+184x^53+77x^54+220x^55+25x^56+48x^57+2x^58+1x^70+1x^76

The gray image is a code over GF(2) with n=424, k=10 and d=204.
This code was found by Heurico 1.16 in 6.42 seconds.