The generator matrix

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

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+72x^49+500x^50+594x^51+882x^52+568x^53+561x^54+258x^55+284x^56+148x^57+110x^58+40x^59+47x^60+16x^61+12x^62+2x^64+1x^66

The gray image is a code over GF(2) with n=424, k=12 and d=196.
This code was found by Heurico 1.16 in 0.156 seconds.