The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  0  1  1 X^2+X+2  1 X^2+2  1  1  1  X  1 X^2+2  1  1  1  2  1 X+2  1  1 X^2+X X^2  1 X^2+X+2 X^2+X+2  0  1  1  1  1  X X^2+2  X  X  2  1 X^2+X+2 X^2 X+2 X^2+2  X  1  1  X  1
 0  1 X+1 X^2+X+2 X^2+1  1 X+3  0  1  3 X^2+X+2  1 X^2+2  1 X+1 X^2+X X^2+3  1 X^2  1 X^2+X+1  0 X+1  1 X+2  1 X^2+3 X^2+3  1  1  2  1  1  1  1 X^2+X+2 X+2 X^2+X+1 X^2+X+2  1  1  1  X X^2+X  1  1  1  1  1  1  3  2  0
 0  0 X^2  0  0  2  0 X^2 X^2+2 X^2+2 X^2 X^2+2 X^2+2  2 X^2+2  0  0 X^2 X^2 X^2 X^2+2  2  2  2 X^2+2 X^2 X^2 X^2  0 X^2 X^2+2 X^2  2 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2+2  0 X^2+2 X^2  0  0  2 X^2  2 X^2+2  0  0  2 X^2+2  0
 0  0  0 X^2+2  2 X^2 X^2 X^2+2 X^2+2 X^2  2  2 X^2+2  0 X^2  0 X^2  2  2 X^2  0 X^2+2  2 X^2+2 X^2+2 X^2+2  0 X^2  2  2  0 X^2 X^2+2  0  2 X^2  2 X^2+2  0 X^2+2  2  0 X^2  2  2 X^2+2  0 X^2+2  0 X^2 X^2+2  0  2

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+30x^48+240x^49+417x^50+550x^51+627x^52+528x^53+551x^54+488x^55+343x^56+212x^57+47x^58+16x^59+21x^60+8x^61+9x^62+4x^65+2x^67+2x^72

The gray image is a code over GF(2) with n=424, k=12 and d=192.
This code was found by Heurico 1.16 in 0.235 seconds.