The generator matrix

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

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+466x^49+902x^50+1182x^51+1186x^52+1360x^53+950x^54+780x^55+542x^56+406x^57+226x^58+118x^59+30x^60+36x^61+2x^62+1x^64+4x^65

The gray image is a code over GF(2) with n=424, k=13 and d=196.
This code was found by Heurico 1.16 in 2.17 seconds.