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

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

Homogenous weight enumerator: w(x)=1x^0+25x^48+22x^50+16x^52+896x^53+16x^54+22x^56+25x^58+1x^106

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 0.094 seconds.