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

generates a code of length 53 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+15x^48+10x^49+24x^50+34x^51+88x^52+684x^53+91x^54+28x^55+20x^56+10x^57+12x^58+2x^59+4x^60+1x^102

The gray image is a code over GF(2) with n=424, k=10 and d=192.
This code was found by Heurico 1.16 in 0.14 seconds.