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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+417x^48+882x^49+1352x^50+1124x^51+1272x^52+922x^53+866x^54+560x^55+424x^56+206x^57+108x^58+12x^59+28x^60+6x^61+10x^62+2x^64

The gray image is a code over GF(2) with n=416, k=13 and d=192.
This code was found by Heurico 1.16 in 0.641 seconds.