The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2 X^2+X+2  1  X  1  1  1  X  1  1 X^2  2  X X+2  2  2  1  1  2  1  X  1  1  1  1  1  1  1  X  1  0 X^2+X  1  X  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X^2+3  1 X^2+X+1 X^2+2  X  1  X X+1  1  1  1  1  1  1 X^2+X X^2+X+3  1 X+1  1 X^2+X  3  X X^2+2 X^2+X+1  2  3 X^2  1 X^2+2  1 X+2 X^2+X  2
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X^2+2  X  X X^2+2  0 X^2+X+2  0 X^2+2 X^2+X+2  X X^2+2 X^2+X+2 X^2+X+2  2 X^2+2 X^2+X+2  2 X+2 X+2 X+2  2  0 X+2 X^2+X X^2+2  X X^2+X  X X^2  X X^2+2 X^2+X X^2+X  0
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  0  0  2  2  2  2  0  2  2  0  2  2  2  0  0  0  0  2  0  2  0  2  2  0  0  2  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+193x^48+478x^49+634x^50+600x^51+547x^52+564x^53+415x^54+304x^55+174x^56+78x^57+65x^58+24x^59+12x^60+5x^62+1x^66+1x^68

The gray image is a code over GF(2) with n=416, k=12 and d=192.
This code was found by Heurico 1.16 in 0.25 seconds.