The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  2  X  2  2  1  1  1  X  X  X  X  X  X
 0 2X  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  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0  0  0 2X  0 2X  0 2X
 0  0 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X  0 2X  0 2X 2X 2X  0  0  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X  0
 0  0  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0  0  0  0  0 2X 2X 2X  0  0 2X 2X
 0  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X  0 2X  0  0  0 2X  0 2X 2X

generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+18x^49+29x^50+24x^51+69x^52+256x^53+60x^54+23x^56+12x^57+3x^58+8x^59+3x^60+3x^62+2x^65+1x^70

The gray image is a code over GF(2) with n=424, k=9 and d=196.
This code was found by Heurico 1.16 in 1.67 seconds.