The generator matrix

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

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+463x^48+128x^49+544x^50+384x^51+1084x^52+384x^53+544x^54+128x^55+414x^56+12x^60+8x^64+2x^80

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 1.48 seconds.