The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1 3X  1  1 2X+2  1  1  1  1  1  1  1  1 3X  1  1  1  1  1  1  1  1  0 2X+2  X  1  1  1  1  1  1  1 3X  1
 0  1 X+1 X+2  3  1 3X+3 2X+2  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+2 X+1 2X+1 2X+2 3X 3X+3  3  1  0 X+2 2X 3X+2 X+1 3X+1  3 2X+3  1  1 3X+2 X+3  3 2X+2 3X  2 X+1 X+2  1  0
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0  0 2X  0 2X 2X  0  0 2X  0 2X 2X  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0  0  0 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X  0  0 2X  0 2X  0  0 2X  0 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+88x^49+205x^50+300x^51+274x^52+328x^53+314x^54+272x^55+122x^56+96x^57+38x^58+4x^59+2x^60+2x^62+1x^66+1x^80

The gray image is a code over GF(2) with n=424, k=11 and d=196.
This code was found by Heurico 1.16 in 0.125 seconds.