The generator matrix

 1  0  0  1  1  1  0  2  2  0  1  1  1  1  1 X+2  1 X^2+X X^2+X  1  1 X+2  1  1  1 X^2+2  1 X^2  1  1 X^2+X+2  1  1  1  1  1  1  1  0  1  1 X^2+2  1  1 X^2+X  1  2  1 X+2 X^2+X+2  1  1  1
 0  1  0  0 X^2+1 X^2+3  1 X^2+X  1  1  X X^2+X+3 X^2+X+2  1 X^2+2 X^2 X+3  1  1 X+3 X^2  1 X+2 X+1 X^2+3  1 X^2+2 X^2+2 X^2+X X^2  1 X^2+X+1  1 X+1  X X+2 X^2+1 X^2  1 X^2+X+3 X^2+2 X^2+2  X X+3  1  1 X^2 X^2+3  0 X^2+X X+1 X^2+X+2 X^2+2
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^2+X+2 X^2+1  X X+1 X^2+X+3  X X+2  1  3 X^2+X X^2+3 X^2+X X^2+1 X^2+2 X^2+2  2  1  3 X^2+3  1  X X^2+X+2 X^2+X+2 X^2+X+2  0 X+1 X^2+1 X^2+X+3  1 X^2+X+1 X+3 X^2+1  2  1 X^2  2 X^2+3 X^2+X+2  1  0  1  1  3 X^2+3 X^2+2
 0  0  0 X^2 X^2  0 X^2 X^2  2  2  0  0  0  2  0 X^2+2  0 X^2  2 X^2+2  2 X^2+2 X^2 X^2+2 X^2 X^2 X^2  2 X^2+2 X^2  2  0 X^2+2  2  2 X^2+2 X^2+2  0  0 X^2+2  2 X^2+2  0 X^2 X^2+2 X^2+2 X^2  2 X^2  2 X^2 X^2 X^2+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+285x^48+940x^49+1582x^50+2084x^51+2545x^52+2296x^53+2170x^54+1792x^55+1187x^56+720x^57+434x^58+200x^59+96x^60+28x^61+14x^62+4x^63+5x^64+1x^68

The gray image is a code over GF(2) with n=424, k=14 and d=192.
This code was found by Heurico 1.16 in 2.05 seconds.