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

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+170x^48+80x^50+568x^52+512x^53+368x^54+288x^56+56x^60+4x^64+1x^96

The gray image is a code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 16.6 seconds.